yes. you could put a (water steam mist thing kinda like the->vicks steamer in your room closes to the bed, the most in the air will keep your throat from getting to dry they sell them at wall greens like 20bucks, but get the one thas just steam with out using the vicks. hope you get to feeling better!! drink some warm tea with lemon and honey it will help south your throat to stop hurting.;)
Once you have strep, you have strep. Nothing can make it worse. The only issue sleeping with your mouth open is your throat will get dry. Please take the entire treatment course of your antibiotics even if you think you are all better. Get well soon!