From grammatical point of view it doesn't look bad at all. I would try to avoid the excessive repetition of pronouns ("She", "doctor"), however, and would split the sentences a little bit more so the structure would look more natural.
Here's what I mean:
I talked to my aunt yesterday. She reported having financial problems due to owing her landlord two months rent. She asked if I could check and see if there's any chance to get help from some social welfare agency. She also said that her doctor has referred her to see another one because of her neck problems.
See how it looks more natural without repeating the pronouns too much?