Assalamu alaykum
In the name of Allah, the Inspirer of truth.
In this time and age it is a luxury to find people who prefer to follow the path of Allah and spiritual progress and protect their honor and faith rather than advance in worldly careers. Allah has obliged children to be obedient to their parents. However, this is as far as the rights of Allah are not violated.
A woman is not responsible to earn; for Allah has placed this responsibility upon the father until she is in his home, thereafter, upon her husband when she marries. Hence, technically speaking there is no obligation upon you to earn in view of the Shari'ah, unless it is an absolute critical situation where only you can be depended upon for the family to survive.
Having said this, since your parents are in trouble, you may try to help them to the best of your ability without compromising your religion, spirituality, and honor. This can be achieved through online or home based work. You may even consider a job where inter-gender mixing can be avoided, as long as you feel you will not lead to degeneration in your din. Working in a mixed setting often leads to compromising a Muslim women's honor and other Islamic virtues and principles, hence as far as possible needs to be avoided. So find some work if you have to where you can preserve your state of iman and be able to contribute.
The following du'a has been considered beneficial for the circumstance your family is undergoing. It should be recited by yourself and your parents:
(35) When one is frustrated about payment of debt,
اَللّهُمَّ اكْفِنِيْ بِحَلاَلِكَ عَنْ حَرَامِكَ ، وَأَغْنِـنِيْ بِفَضْلِكَ عَمَّنْ سِوَاكَ.[1][1] [1]
[1]All�hummakfin� bihal�lika 'an har�mika wa aghnin� bifadlika 'amman siw�k.
O All�h, suffice me with lawful livelihood adequate to my needs instead of ill-gotten livelihood, and graciously grant me freedom from needing anything from anyone besides Yourself.
Note: Whoever recites this du'�, All�h will assist him in repaying his debt even though it may be the size of Mount Sabir (A mountain in Yemen).
May Allah strengthen your iman and resolve to follow His path, and deliver your family from this compromising situation.
Wassalam
Abdurrahman ibn Yusuf
taken from sunnipath