Electrolysis would be a great option for the removal of the hair on your upper lip, Rogue. Just to reiterate what redhead has said, one treatment is not enough. Alas, there is nothing on earth that will permanently remove hair in one treatment.
On average, I need to see a client 6-9 months at regular intervals so we can get through 3 hair growth cycles and catch all the noticable hairs that come to the surface. I like to see a client every week to two weeks in the beginning so we can get to that first clearance and then maintenace sessions kick in where the treatments are spaced farther apart, say every 3 weeks then every 4 weeks, etc. Permanency follows soon after and then we’re finished. You may need some periodic cleanups (1-6 times per year)for a few hairs that pop up due to any hormonal issues
you may have. These sessions are usually very short.
As for swelling, if treatment energy is correct, if the time treating the upper lip is limited to 20 minutes (for some, 30 minutes is okay) and the work is scattered so that close neighbor hairs aren’t being zapped, swelling should not be an issue for more than an hour or two, if at all.
Definitely use 100% aloe vera immediately after treatment (even if you have to take it yourself), followed by an ice pack wrapped in gauze for 10 minutes. If you wrapped the ice pack in tissue, the tissue will stick to your freshly applied aloe vera.
As redhead advised, seek a professional electrologist(s) you can work with to solve your problem, keeping in mind that you must be consistent with your appointments to gain anything good from permanent hair removal.