"Waste of time"

I went on Monday the 8th of April at 8am to register. I was told to register at 2pm. I returned at 2pm and was told there were no registrations on Mondays. After asking different receptionists, the truth emerged that they could register me. The receptionist asked me for my address and photo ID. I presented Council Tax and my drivers license. She then said she needed my passport and could not register me. I then asked different people and the truth emerged that they could register me if only they have my previous doctors/GPs. Eventually I was getting registered. I advised my chest was infected and I was not able to sleep for long before waking up to severe uncontrollable coughing from my lungs. However, they can only see me in 3-4 weeks. I've been suffering for 3-4 weeks and I rarely go to the dr so why can they not see me for a service as a tax payer we pay for? To my surprise when I saw the nurse today, she said I could see a Dr today, instead she secretly insisted she wanted blood tests first. It's obvious I need some sort of medication for my lungs so why can they not see me and prescribe me?