Yes, you could have hemorrhoids. You can get them from straining to use the bathroom. They can itch, burn and cause pain.
And yes, you could have a prostate problem. It usually happens in older men but it can some times happen in younger men too.
I'm glad you will be getting checked out soon. In the mean time, get an ointment for the possible hemorrhoids. It should not hurt you to use it even if hemorrhoids are not the problem. If they are thought the ointment should give you some relief.
Buy a natural stool softener so you'll be able to use the bath room easier.
I wish I could tell you what the pain is about but I'm just not sure.