You could ring the surgery and ask if they have an appropriate appointment. Maybe with a nurse practitioner.
I have to say though, I'm usually fit and healthy, exercise hard nearly every day and colds are usually a mild sniffle. I am going to exercise today for the first time in 5 weeks. About a week before the easter holidays I caught a cold. It went on and on and on and on. I had the terrible, face, teeth, ear pain. My face throbbed, I couldn't breathe. I was exhausted, sore throat, terrible hacking cough unlike anything I've ever had before. I didn't eat, could barely face walking down the stairs some mornings. DH took a day off work for the first time in 16 years. He struggles in through everything. At one point, I didn't leave the house for 8 days. When I emerged, blinking, into the real world, I met several friends, all thinner, pale and having spent a few weeks with precisely the same thing.
My sinuses were the main problem. Long after the other stuff was clearing, my sinuses were terribly blocked and slightly leaking down my throat which was causing the cough and sore throat. Suddenly, 4 weeks in my sinuses decided to drain. It was hideous. The most foul tasting/smelling bright yellow/green stuff and so much of it.
It's all gone now and I feel normal. Unfit and out of shape but all better.
DH and I agree it was the worst 'cold' ever.