...will keep some "reserved" appointment times for more urgent matters, or will have some time each day when they don't usually schedule people for (doctor's documentation time or something) when they can, at their discretion, squeeze someone in. Once you find someone who is accepting new patients and that you are going to make an appointment with, talk to the person who is scheduling you (who likely has at least a little medical knowledge even if they aren't a full fledged practitioner themselves) to see if they think you need to get in sooner and if that's a possibility. Explain the nature of your symptoms and your concern that it's already been going on for a couple of months and that you are worried about waiting another entire month before being able to see someone. Either they will reassure you that they think it's okay to wait, or they'll schedule you in one of those "reserved" spots sooner, or they'll tell you that they can't possibly get you in any sooner but that you shouldn't wait and you should go to an urgent care center or your school's clinic or something to get immediate priority.