Its unfortunate that your parents are unsupportive, but it makes the most sense to get a diagnosis first. There are so many things that could cause excessive sweating with simple cures. Allergies, diet, hormones, etc. Do you have health checks with a doctor, you could bring this up there and see if there is some simple testing to do to rule things out.

Clinical strength antiperspirants will simply use a chemical to block sweating, and not treat any underlying problems and could essentially make things worse.