Assalaamu alaikum my dear,
(gently) I understand you, my dear. You feel such a pressure to look after this little person, but you have nowhere to go and no-one to help you. You feel that you can't take any more, and that here is no way out of your problems. I know this feeling very well. (smile) The good news is: there are ways out. You just can't see them right now.
First of all, my dear, you need to get some food into you. If you haven't eaten for a couple of days and your stomach is in knots from stress (and pining perhaps for your husband?), you won't feel like eating at all. But you must force yourself. Your child's wellbeing depends on you getting yourself together. Do you want him to grow up as lonely and helpless as you (or worse, maybe)?
He's so beautiful and loveable, isn't he?
Try some honey in warm water (or sugar, if you have no honey). Then if you can, eat light, sweet things to start with. And go slowly. As if you're breaking a fast (because you are!). If solid food seems insurmountable, you can get some special drinks at the pharmacy called nutritional drinks. You can find brand names like Boost or Ensure, or your pharmacy may have an in-house brand that is cheaper. Ask your pharmacist. Actually, try to find a sympathetic pharmacist, and explain your problems with eating because of stress. If you are breast-feeding, let him or her know this. He or she may be able to recommend various things to you.
The nutritional drinks can help give you some more energy. You need energy to deal with your baby and get yourself the help you both need. They can also help wake up your stomach more gently, so you can get back to eating regular food.
I don't know your financial status. I don't know your family structure. And I'm not very knowledgeable about services given in your area for new mothers. But I'll try to give you a few ideas.
First off, forget your ex-husband for now (even if you really care about him, obviously, he doesn't care about you or the baby; otherwise he wouldn't have abandoned you and your child). He is, I suspect, just an additional source of stress.
Think over your family. Is there anyone who would help you? Put your pride aside: is there anyone who you can stay with, at least for a few days?
If there is no family support, do you have any neighbours? Friends? They may not be delighted at helping you (sigh. Everyone is so busy...), but they may help you out a bit. Try asking. You may be surprised at how people (even strangers) can be kind. And they may be able to point you towards local community services.
Do you have a masjid in your area? Can you ask the local ladies to help you (I'd be careful of the men, if I were you. While some men are really nice, there are certain sorts of men who prey off vulnerable women. And you are very vulnerable). If there is no masjid (or they have few services), try a local Christian religious community. In my area, the Catholic church has many services, and they help, regardless of your faith. Look for established Christian communities. Avoid recent churches, or churches that are unknown to you. There are some rather bizarre communities out there, that a vulnerable person should avoid.
Are there any social assistance-type services in your area? You might try googling for these. There is the LaLeche League for breastfeeding mothers. They may be able to point you towards some help.
Please avoid googling for your son's health. This is just going to drive you crazy. You don't have the knowledge to sort through the signs and symptoms, and there are so many potentially terrifying diseases that they are likely to overwhelm you. Use common-sense, instead.
I don't know your son's age, but newborns very typically get acne-like spots. Its very normal. Look at your son: is he wetting his diaper frequently (the exact frequency varies with age. This you can google)? Is he active? Is he nursing/taking a bottle frequently? Does he seem like a healthy young lad? (Forget the spots. Just look at his general well-being). If he seems lethargic or he's not eating or he's not wetting his diaper much, take him to a hospital. But if he looks pretty energetic, feeds enthusiastically and peeing normally, he's probably ok. Go and see a doctor, to ease your mind, and rule anything out. But if he looks healthy, he probably is. Learn to trust your intuition. You are a new mother, so you don't have a very strong intuitive sense of your child, as yet. But you have it a little, I'm sure. Try to step back and look at your baby: if he seems unusual, take him to see a doctor. If he seems usual, he's probably fine.
Doctors are sometimes hard to see. Pharmacists are a lot more accessible. What they are allowed to do varies from place to place, but they have some specialized knowledge, (smile) and have probably seen a lot of nervous new mothers (it happens to us all, you know, my dear)! If you're not sure about something, and seeing a doctor is hard for you, try a pharmacist. They are trained to see danger signs (at least, in Canada and the US I know this to be true. I'm less familiar with other countries). And they are trained to deal with minor issues themselves. He or she may also be able to refer you to local services for new mothers in need. Don't be shy to ask. And if you have the misfortune to land on an unsympathetic pharmacist, go and see another (and this goes for neighbours or various service providers, or whoever. Everyone has a bad day, sometimes. If one person lets you down, try another. Be a tiger, my dear. Your baby depends on you).
But first: look after yourself. You are a precious and unique human being. God put you on this earth for a reason. And now, He has Entrusted you with a baby. (smile) You can do it. Even if you are alone, God will send you some form of help. Hajar was alone with baby Ismael in a desert. It happens, sometimes, that we mothers are alone. But Allah Sends help. (smile) We don't all get Zamzam water, but there are people and circumstances out there that can help you. And you will find that you have more inner strength than you may realize. Call on Allah to Help you. Beg Him. And then trust in Him. Take care of yourself. Go out, look for help. You must make your efforts. And then, leave everything up to God.
Please, when you can (after dealing with your health), let us know how things go. And if you need to talk to us, or ask anything, please do. (gently) But talking and asking people who are closer to you is likely to be more beneficial. I can't hug you in person (which is what I would do if you were here), and I don't have the local knowledge of services that someone in real life around you has.
Hugs, my dear. Hang in there. You can do it.
May Allah, the Gentle and Loving, Strengthen you and Help you to be a wonderful blessing to your son... and he a great joy and blessing to you.