I recommend making a visit to the new high school so you can become familiar with where things are at. Chances are there are bathrooms all over the place, so you'll never be very far from one. If anyone asks you about going to the bathroom a lot, just say you had a bladder infection recently and it makes you have to pee a lot.
Your mom needs to trust you when you go to her with a problem like this and asks to see a doctor. Tell her that one day she'll be older and you may be making medical decisions for her. She'll want YOU to believe HER, right? ;-)
You might want to reconsider not wanting to see a therapist. You don't want to live the rest of your life with this burden. Best to get it addressed while you're young, before it becomes really deep-seated. God bless you!