For severe tooth pain such as in the case of an abscess, the only thing that has worked for me is 750mg daily Amoxicillin. I have tried clove oil which is extremely powerful but does not kill the pain even if you drink the stuff and can make the pain worse as an abscess is about pressure build up from toxins under the tooth and so needs to be burst in some way.
I rubbed my tooth-brush rigorously on the abscess itself which hurt a lot, but tons of puss and blood came out that needed to come out as it is poison and what causes the pain in the first place. The colour of the puss is like a dark yellow/orange and there is often a huge amount of it if the abscess is particularly large in size. I could not burst the abscess any other way and this is the only real way of doing it and without seriously hurting yourself or your gum.
For general tooth pain not caused by an abscess, the only thing that will stop pain, is medication unless the tooth pain is mild enough to bear it. Very few people can cope with pain and so the ones that can't, they need something that is going to work and that only comes in the form of pills - not garlic, cloves and things on here that are for more tougher folk with stronger pain threshold.
I cannot cope with tooth pain at all and often suffer from abscesses and I have tried everything out there and nothing works except only for strong antibiotics. A mild tooth ache is another thing and anything will work for that as long as it stings and draws out the source of pain such as warm salt water. Dental pain comes in many forms but the worst is by far toothache caused by an abscess and to which the only cure is relief gained by bursting as much of it as possible and with an object that isn't going to cause damage. The toothbrush is the best and only real sure way of bursting an abscess It takes some pounding on the gum with the bristles to break the top layer of the abscess skin, but once you have done it and the puss and blood come, you know then that you have begun to relieve yourself of the pain an abscess does provide.
I talk from experience and with common sense.