"How can all appointments be filled in 7 minutes"

have a bad chest infection, I have a history of these leading to pneumonia, having spoken to the nurse I was told that if there was no improvement in 7 to 10 days I should make a gp appt. On the 10 th day at 0800 I telephoned the practice, I was 9 in the queue, at 0807 my call was answered. I was told that all appointments were filled as were telephone appts. There was no one able to see me and I should try again the following Monday. I cannot understand how all practice appointments could be filled in 7 minutes. I am afraid that I became another burden for the hard pressed A and E. I feel very shocked and a bit anxious that I as an older person cannot access GP services. There we are that was my experience.