I have had a permanat crown put on around three weeks ago. I had severe pain afterwards and my dentist gave me amoxcillilin to clear up a infection. It cleared and for several weeks but within the last few days I have had the severe pain come back. I went to by dentist yesterday and he said it will be the same thing another infection. I have taken 4 tablets now three yesterday and 1 this morning and the pain is not going.
I have ear ache
Slight head pain
Bad eye and mouth

When I drink cold water and swill it over the area of the pain the pain goes off for a minute and then comes straight back.

Teeth are a pain no pun intended. If the pain doesn't away after this pill regiment I would see another dentists for another opinion. Meanwhile I would use some ice cubes on that tooth if its just a nerve problem and no low grade infection then the pills probably won't work this time. Think of it from the dentist point. My patient has problems with his crown and to cover his bases which is fine he prescribes low dose for infections just in case that what it is. He might be right and the first treatment didn't quite get it. If that's the case it took some time for the tiny infection left to build up enough to feel it again. The cold water obviously is calming down a nerve, Take your pills and ice the crown on and off through the day and night to give that nerve a chance to calm down. At the end of the pills see how it feels. If its not good see another dentist for another opinion
Happy Holidays! Singed 21boat.

Have your dentist check the bite, the crown could be high. Take some ibuprofen (Advil) if you can, that may help with the inflammation.
If you have an infection in the tooth, you should be having a root canal done and not just being prescribed antibiotics. Maybe it's time for a second opinion??