I feel your pain, OP.
The pain I had with a dental abscess was the worst I've ever had and I've had over my share of traumatic injuries.
I wanted to beat the pain out of my head by banging my head against the wall. I still live in fear of having another one.
I would go. You've been in too much pain for too long. Plus infections in the head can be dangerous.
The worst they can do is turn you away.
What on earth is going on with the NHS that they can't treat someone in as much pain as you must be in.
If they won't/can't help in any way, ask your GP for a private referral. You might not be able to afford it, but you may get the sympathies of a consultant who would be willing to get you in as an emergency case.
I have no idea if that would work, but I'm at a loss at what to say to really help.
If you can get to the hospital first thing in the morning rather than in the night where they're having drunks to contend with you may be better off.
I wish I could wave a magic wand and relieve your pain.