I had a slipped disc at 16 and was operated on at 18.
My husband had a slipped disc from his service in the military and was generally manageable, but one day he was exactly as you described you have been today. His med centre military GP pumped him full of strong prescription medication and I gave it to him like clockwork for 24 hours, as he cried and rolled around the bed, it was horrendous.
In the end he couldn't stand make it to the toilet and I called an ambulance who gave him gas and air and IV paracetamol and took him in.
After a lot of arguing between the Consultant and I we got him admitted for a few days and he was given pregabalin, tapentadol and oramorph to deal with the pain, then booked in for a root nerve block in order for him to be well enough for us to get married, then when we returned from our honeymoon he went pretty much straight into surgery.
My argument was that they initially gave him tramadol, which had no effect whatsoever and they were still going to send him home. As a health professional myself, I would be negligent if I sent a patient home in that state and I really had to advocate for him.
Sadly we experienced one cock up after another with how the military initially handled the slipped disc when he first presented to the med centre, and he was awarded a five figure sum in compensation.
If you are screaming in pain and need further medication I would urge you to go to A & E at least just to manage the pain until you can see a GP and go through the referral channels.
I feel for you though, it's absolutely shit.