Dentists often won't act if there's an infection present (which your mention of antibiotics suggests there maybe) for fear of the infection spreading into the patient's bloodstream and leading to sepsis (which can be fatal). So there might be a very good reason why no action is currently possible.
However, if your bank balance (or credit card) can take the hit, it might be worth phoning private dentists in your son's area and asking if they can offer immediate treatment and whether they'll let you pay by providing your card details over the phone. (I'm assuming that you don't live close to your son). You can search for dentists in his area on Yell:
https://www.yell.com/
It could also be worth asking your son what type of painkillers he's been given and then asking a pharmacist whether anything stronger (and/or which can be taken in conjunction with what he's already got) is available.