If you're dealing with an infection that's gotten to a point where you're in constant pain, I would suggest you seek immediate medical attention. You don't want it to turn into sepsis.

That being said, I recently saw my dermatologist for an infection. He prescribed me Cephalexin and said that it was particularly effective at clearing skin infections (which sounds like what you are dealing with since it's from a tattoo). The Mayo Clinic states that SMX-TMP is primarily for treating "urinary tract infections, middle ear infections (otitis media), bronchitis, traveler's diarrhea, and shigellosis (bacillary dysentery)". [1]

If seeing a doctor is not an option, there are also over the counter antibiotic ointments such as Neosporin (or Polysporin) which may help. But seriously, it sounds like you're in a bad place, I suggest seeing a doctor if you can.