You're 18. It's normal.
As far as equipment is concerned, you might get a better result from a jock strap. Oh, it'll be uncomfortable, but you just have to weigh the physical discomfort against the social discomfort. Realize that it's only a temporary solution. You will eventually "acclimate" to the situation, so to speak, and the crutch can then be discarded.
I think, though, really you should talk to your teacher about it. If it's creepy you're worried about, jumping through hopps to conceal your situation might come across creepier than having an earnest discussion. Make sure you bring it to your teacher, because he/she will handle it with maturity and understanding. Your partner may or may not be enlightened to the situation, but leave that to the discretion of the teacher.
You can also request to change the choreography, at least for now. If you are in cahoots with your teacher, and it is decided that it's better kept a secret from your partner, then the teacher can invent some excuse for you as to why it should be changed.
And, well, there is also one other obvious thing you can try, but, this being a wholesome web site, I'll leave it to your imagination. ;)