This isn’t as simple of a question as it may seem. Since you didn’t provide the medication name it’s not possible to look up any side effects of that specific medicine. Usually, if it’s a listed side effect it’s the consumers responsiblity to note that and accept the risk. If anyone was liable it would be the drug company.

you could file one but probably would not get anywhere, there are usually warnings on it for side effects

You need a good lawyer, one who won’t take advantage of you. Go to the website BestofUS.com, look under Personal Injury, your city and state. Call him or her and tell them what happened, they’ll tell you if you have a case. This website lists the best professionals in 10 fields, law, medical, finance real-estate, dental even vets.

You can sue (it is not clear if you will win, though).

You need to look at the list of side-effects for the medicine to see if hair loss is listed (better for you if it is not).

maybe, does the medication you were on list any side effects?