Assalamu alaykum
First of all, sis, there is no need to work yourself up or worry. I am sorry to say but I would question your uncle's judgement on your condition, you know him better than I do, but to diagnose someone with 'blood cancer', without performing any blood tests is something I wouldn't imagine a professional doing. And even if he was suspicious, I don't think he should have told his fourteen-year-old niece without confirming it first.
But as he has told you, and he is an oncologist, I would suggest you should have those tests done. I do not know the fiqh perspective from it, but as a Muslim life is sacred, we should do everything in order to preserve that life - look back to the Islamic Golden Age, Muslim physicians and doctors were the leading authorities in disease prevention, diagnosis and cure. This is because of the teachings of Islam, for example:
‘“Allah has not sent down any disease but He has sent down a cure for it.”Narrated by al-Bukhaari, 5678.
There is a cure for every disease except death, and I believe to refuse having a possible problem diagnosed and hence delaying treatment would be a misjudgement. You should not wait around for death or for Allah SWT to miraculously give shifaa - this isn't how it works. And this does not compromise tawaakul - the same way eating and drinking does not compromise tawaakul. It is our duty to ensure we remain in the best of health, and within halal means heal ourselves when unwell. This is faith in Allah SWT, when following His commandments we use the means He has provided for us on this earth, tawakkul should not make one fatalistic or helpless - that mindset actually goes against this concept.
So go for those tests if you are concerned. To be suspicious and not go may not be suicide, but it would be ignoring the means Allah SWT has provided mankind with to heal themselves, and that would be wrong, because it is His mercy that He has given the cure for ever disease - we should protect life to our highest ability.
And also, you are not unloved in the slightest. We all love you, and most of all, Allah SWT and His Messenger (pbuh) loves you more than anyone here could, and that is all the love you need.