If you are having a problem/worry/new sympton, not feeling well/feeling worse etc, and you are worried about it and want to have checked out, how long do you usually have to wait until you get an appointment with your doctor?

I've been having some new sinus/nose issues/symptoms lately and coupled with feeling crap (extremely bad fatigue, feverishness, joint pains that wont go away etc) I am a bit worried and want to see my ENT and Rheumatology doctors. I called to book an urgent appointment with my ENT today and was told there are no appoinments at all until the 15th August. I haven't tried the rheumy yet so will see what happens there but I think that is very bad. The 15th is almost 4 weeks away? I know I could always go to A&E if things were that bad but they probably don't have a clue what Wegs is or what to look for, besided, my nose issues aren't "a&e" type problems.

Am I overreacting or is the wait time for an appoinment quite bad?