Is there a way where I am able to be compensated through my mother's TRICARE and Medicare for the home health care I’ll give her?

No, you cannot be paid almost certainly and not by insurance companies. Medicaid will sometimes compensate family members for providing care, but very little and certainly in no wise enough to replace anything they might have earned from a job. When we see this happen, people moving in with elders and caring for them they often end with no place to live, broke, without a job history, and broken in mind and body.
I don't know what you have done about POA but if you don't have one and mom is no longer competent to make her own decisions you may need guardianship or conservatorship to manage things for her, another costly problem.
I wish you a lot of luck, but know too little about your individual situation to say too much more.

Not an option. She would literally die

https://www.agingcare.com/articles/how-to-get-paid-for-being-a-caregiver-135476.htm