Is it okay for me to use a towel as a night-guard for my teeth?

I do not. Recommend that, that can cause you further problem an even effect on your breathing at night.
No. See your dentist and get a proper one made. A towel doesn't stay in place, can gag, and is inefficient.
Absolutely NOT! A towel makes a horrible night guard. You could choke or strangle yourself. Think about when you are sleeping and roll over, very bad idea. Towels are designed for drying only. Precise fitting mouthguards, made by your dentist are what you need and should get.