Help me, she's teething!

I am presently so sleep deprived that I am surprised I have the energy to type. Wait, go back - I'm so sleep deprived I'm even surprised I have managed to find the laptop's ON button in the first place!

My 3month old is teething. Yes, teething. My mother-in-law managed to diagnose it over Skype (gotta love Skype), but I told her that it couldn't possibly be the case. Three month olds do not teethe! Do they?

Frankie was showing all the classic teething signs; drooling like a Pavlovian dog at supper time, more grumpy than a Snow White dwarf, biting down on anything (and everything!), and so irritable at night that she won't sleep for more than an hour at a time.

At first I worried about my milk supply. Maybe I wasn't producing enough? Was she simply going through the infamous three month growth spurt? The constant feeding would point to that. But growth spurts are supposed to last only a few days and Frankie's mood swing was worse than a hormonal teenager's, and it had lasted well over a week. What to do?

After the Mother-In-Law-Knows-Best Skype call, I decided not to rule out teething simply because of my wee-one's age, but to have a feel around and see what I could find.

Frankie was more than happy to let me go all 'Indiana Jones Explorer' in her mouth, because every few seconds she'd get to heartily chomp on my finger which seemed to provide some comfort. Eventually I found it - her tooth had already cut! It wasn't in the standard spot for first teeth - it was on the left and quite far back. But there it was, none the less. My little girl's first tooth!

The next day the doctor confirmed my diagnosis and suggested some Nurofen or Paracetamol for bubs. But so far, there's been no relief. I'm still getting up more times in the night than a pensioner with a bladder problem. Feeding seems to be the only thing to soothe her, but I physically don't know if I can keep it up.

And herewith goes my first call-out to all the parents out there.... can anyone suggest how I can help get my bub to sleep during this painful teething process? I'm literally at my wits end and hate to admit I'm not coping well, but just when I thought Frankie had managed to sleep through the night this has happened and I'm beginning to worry I'll never know a full night's rest again...

HELP!