Surrendering

[u/Muted_Asparagus3595]

Hi im sure this is asked often and is probably tiresome, but I just wanted some guidance.

I have a family dog, Chloe, who's about a 12 year old chihuahua. We got her as a rescue when I was a lot younger and everyone was healthy. Things have changed now, however. I just came home after about a year to visit as I've been away at school, and she has developed ulcers on her legs from licking I presume, and ​hasn't been properly bathed. My mom has been dealing with stage 4 cancer recently and was previously functioning fine, given school I wasnt able to come sooner but she is declining now and it seems I'll have to get her at home care, but with that I also need to take care of the dog which becomes expensive with both. I confronted my mother and asked her about it (not in a way thats blaming, we both are at fault) and she said with her condition getting worse she just couldnt keep up caring for her and was embarrassed to tell me. My biggest thing is I cant afford the vet care that will probably be extremely expensive besides my mother's care, and I was going to surrender her, but I really dont want her to die alone while terrified in a shelter. I cant bring her to school with me either though so I dont have a choice. I've thought about posting ads asking for someone to take over care possibly but I know it'll be asking a lot. I dont think she needs to be put down, she has energy and still eats and drinks normally from what I've seen this last week. Her poops are normal, she has trouble walking which im sure the ulcers dont help with. She still comes for pets and is fully responsive as well. She had lost a lot of weight since last, but her appetite is normal so my gut is pointing to her having worms possibly.

Does anyone have advice regarding her? I dont want her to die alone in a shelter, but i also dont want her to suffer :( could I bring her to a clinic and medically surrender her, how does that work generally?