Looking at the growth on the hoof wall below, there is altered horn, meaning the where it's growing out has been damaged for a while.
About cutting into abscesses: Don't. If you cut into it, you are introducing more bacteria and such into an already weakened area, which can make it take even longer to heal. As hard as it is to see, it's better to let them get through it on their own. Once their body is ready to let it "blow" then it's isiolated the pocket of pus and it's no longer an entry point to the blood stream, so the exposed hole not a problem. Much like squeezing a pimple before it's ready, you often make it bigger and it takes longer to heal.
If the abscess is on the sole, it's a good idea to pack the hole with cotton balls soaked in idodine and wrap the foot for a couple of days, since the bottom of the foot in domestic horses does tend to be exposed to a lot of manure, to make sure the hole is sealed to the body.but hairline blowouts heal on their own. You can put corona or furacine ointment on if you feel you have to. Oral anitbiotics are usually fairly useless for a self blown abscess, since the body has blocked that pocket off.
Could be that cutting into it introduced more germs, that formed yet another abscess. Sometimes the hairline ones don't drain as fast, so can seem to take forever.
Abscessing usually stems from a stone bruise, complications of laminitis or being quicked by a nail from the farrier. If the pic is of your horse's foot, looks like there's some rings on wall, usually indicative of laminitis, and they can have mild bouts you don't catch, but the walls tell.