Hi there Siahues, and welcome to Scarleteen!
That's a pretty tough situation - I'm sorry to hear that you don't have a whole lot of privacy. While it may be something that goes against certain religious beliefs, masturbation is something that lots and lots of people engage in throughout their lives, and is perfectly healthy and safe. (In fact it can be good for you! Check out Going Solo: The Basics of Masturbation
for the scoop.)
Other than showers, the only other suggestion that I have would be taking baths, if possible. It's hard to really enjoy yourself when you only have 15 minutes or you're afraid someone will walk in at any moment. If you say that you're going to take a bath (if you have a shared bathroom - otherwise you don't necessarily have to announce it), others will usually give you a little more time and space than they would a shower.
That is one of the benefits of living on your own or having your own room in a shared house. Have you ever considered or tried to advocate for something like that?