>>3834 No no you can get all kinds of stuff that'll numb you up good over the counter. In fact pharmacists know a lot more about treating you than you'd think. Go in there and explain to the chemist exactly what it is you're trying to do, and while they might say they'd recommend you visit your GP to repair your lip, they'll also choose the best numbing agent for the job if you push ahead with it yourself.
>>3835 Anbesol is also a very good topical anaesthetic, but it wears off after 5-10 minutes. If you can reapply it it'll do a bang up job for what you need it for. Failing that, cocaine and ketamine are both great anaesthetics - I've used both to successfully numb the pain from swollen gums, and make my night more interesting.
But yeah, you should probably go along to your GP and get them to hack your lip up.
Whether or not ketamine is a local anaesthetic you certainly shouldn't be performing surgery on yourself while on it. OP's best bet is probably benzocaine, which is what's in most anal lubes local anaesthetic gels anyway.