25 yo female androgenetic alopecia with red burning scalp, what's the solution?

In  my opinion, the redness on your scalp needs to be evaluated. A large percentage of women with androgenic alopecia have inflammation. Inflammation is a cause of hair loss. I would suggest a biopsy of the scalp. Once a diagnosis is obtained, appropriate treatment can be instituted by  a hair loss expert.
PRP hair md.com

There are many reasons for burning and I’d need to see your scalp up close to determine why. A biopsy might even be needed to confidently rule out a scarring alopecia as well as other potential causes that could have been missed. If the burning is not coming from any specific pathology, you might fit the definition of so called “red scalp/burning scalp syndrome.” These are hard to treat sometimes but options include topical steroids, oral gabapentin, topical gabapentin, oral amitryptyline, topical capsaicin. Avoiding harsh shampoos is important. Please see a dermatologist if burning persists.

Lichen pilanopilaris is one if the condition where u may find burning sensation but redness is not diffused in it....Go for biopsy..it's diagnostic