Take a paracetamol or diklofenak pill and place it on/under the tooth and hold it there, let it dissolve on its own and it will have some effect as a topical analgesic. That's what I've been told at least, not to numb it enough to pull out your own tooth but to make things more bearable until you can get to a dentist.
If your tooth is busted and broken already then I don't think you'll get all of it out, instead leaving the root exposed and thirsty for sugar and yearning for infections. And you will not try to dig around in the gums to get everything out.
Go to a dentist for a cheap checkup and when you're there explain that you're a poor retard then ask if they can pull it on the cheap if they get paid under the table.