What if I walked into the wrong bathroom?
That is awful. Did you know that was the wrong bathroom?
Yes, but I thought it would still have a stall.
While you made a big mistake, you are willing to own up to it. With that said though, you knew that you were making a mistake and did it anyway which still makes it wrong. You shouldn't do things that you know are going to become problems later.
This problem wasn't completely my fault. The school should have a bigger sign near the toilets.
Sign or not, you still knew that you shouldn't have been there. Just admit it and try not going in the wrong bathroom in the future.