Firstly, HUGE empathy here, have suffered horrendously recently with wisdom tooth pain, and two other teeth at same time.
If you have an infection,you will have to have antibiotics before they will even do anything to you, as there is a risk of sending the infection into your blood stream and causing other systemic infection - particularly myocardial. Which you don't want.
For immediate pain, get yourself some paramol, which has dihydrocodiene in it AND paracetamol and also take with some ibroprofen ( i got the expensive fastest acting on market!) but normal will do. It is a very good combination and any pharmacist worth their gold will suggest this combination.
Secondly, get an appointment at the GP emergency appointments, call your surgery, they will have a number OR your local hospital minors or even reception will be able to give you either a local on call surgery/GP or even book you in to get some anti biotics which is what you need ASAP. Truly, a dentist will do exactly the same, prescribe anti-b's & get you to go back when course finished & pain stopped. You are MORE likely to find a GP on a saturday than a dentist, plus they are free
IF you can not find anywhere and end up going to a&e Trust me, severe toothache is not dismissed as trivial, it's known to be incredibly painful and you won't be looked at as a time waster. My local A&E has an out of hours GP service attached. YOu don't need a dentist to tell you if you have an infected tooth, your symptoms will tell them!
Lastly, if you have any clove oil, dab on, around the tooth, anywhere you can bare, with a earbud, or I found even better my DD's Anbesol, which we used for her teething. The liquid version. If you don't have any at home, go to chemist in morning, and when getting analgesia, get a bottle of anbesol too, the liquid, NOT gel, the gel is useless and just smears anywhere but where you need it - just like when your child is teething!!
I really really hope that helps PLEASE, as a veteran of such things take my advice- its very very much tried and tested. I eventually last time, had my infected impacted wisdom tooth extracted, stitched etc, then the next day 2 more taken out... very horrible indeed. Oh, then got an infection in the wounds as my DD was taken into hospital with suspected meningitis for 4 days, so I didn't look after the "holes" very well! SO for gods sake if you have it removed, look after it, and rinse it with saline every hour or two & after any food!
I've gone on YET again.. sorry! but it is all valid - just for a change!