Given that you are syringe feeding Merlin, as long as you give the medicine along with his food and some water, I don't see why Merlin should not be given pain relief. That theory would apply to all medications, not just pain relief, so I wonder what the vet would do if Merlin was in need of antibiotics or other oral meds...
Naturally there are varying opinions on what is good and what's not, but in cases where the vet absolutely refuses to give any pain relief, you are left with little choice - either find a much better vet very quickly, or do something yourself!
There are two things you can try:
1) Infant Calpol/Childrens Nurofen. Dose is usually 0.2ml up to twice daily. This is used as a general painkiller, usually when the vets refuse to give any pain relief to pigs clearly in need of it!
2) Daktarin Oral Gel.
This is the one I recommend for dental oral trouble. It is not a painkiller, but it works well at soothing the mouth where overgrown teeth (or an oral infection) has led to a sore mouth and discomfort eating. I have found that even pigs with minor molar overgrowth refuse to eat for a couple of days after treatment, simply due to the discomfort the overgrown teeth caused. A dose of 0.5ml of Daktarin, given twice a day for 2-3 days after the treatment, soothes any sores and generally - in my experience - gets the pig eating on his own quite a bit sooner.
Both should obviously be used as short-term as possible, but Merlin won't get anywhere if pain is causing him to stop eating, which means he doesn't wear his teeth down with hard food and you could end up starting all over again!
I'm sorry the vet wasn't helpful in terms of easing the pain. Were the teeth corrected?