Sorry things have been tough. I know what you're going through.
About Nystatin. No personal experience w/ it, but a dermatologist taking a skin culture could determine if Nystatin should be prescribed for you. Whether you plan to redo the treatment or some other home remedy, make an appointment with the doctor immediately if you haven't already. (Some people have successfully used otc anti-fungals such as Tinactin. But again don't completely go alone here, get a professional to take a skin culture.)
In answering your other questions. . .
-The inventor of the above treatment didn't recommend an antibacterial soap (not necessary), just a concentrated dish washing soap. However, the soap you're using should do the job.
-Yes, any bowels will do as long as you disinfect them. If you're using a sink, best to wash w/ soap and a sponge each time before steps 7 & 9.
-Yes, tube of jelly is fine. In a used jar, many hands w/ many germs could've been going for the jelly.
-Yes, repeat steps 2-10 to wash off the jelly.
Okay, I have a feeling you've been pretty much following the steps successfully even if you weren't following completely to the letter. The aim of the steps is to kill the infection. Afterwards, you need to heal your cuts. Protect your cuts and your lips always.
After cleaning off the jelly to determine everything has worked, I would apply regular ointment on the cuts and jelly on the lips. Probably would skip the beeswax for now. If you're home alone before sleep, put band-aids over the cuts. The strips' adhesive shouldn't be too tough, but enough to constrict your mouth to remind yourself not to open your mouth wide. Band-aids act like a second skin. Cover your cuts w/ this second skin and your cuts will heal faster (just like ordinary cuts).
In the morning very gently clean your mouth with warm water and peroxide. Reapply with ointment and jelly and reapply the jelly (when your lips dry) when you're at work. The jelly is a shield against saliva, sweat, heat, dirt, and food, anything that can reopen the cuts. Heat will especially dry out your cuts which should be avoided. Anytime during the day you find there's crap on your lips, go to the restroom, cup your hands in warm water and bathe your lips in it. Pat them dry w/ paper towels and reapply the jelly. When you go home, before sleep reapply the band aids.
About food and drink. Don't let irritating foods touch your cuts. Buy a bunch of straws and bring them w/ you. Whether its juice, water or even alcohol, drink it with a straw. Instead of eating out during the day, prepare your foods in tupperware and bring them w/ you in a cooler. The food should be cut up in small pieces. Avoid food that's salty, spicey, or acidic (oranges, tomato sauce) because they'll reopen your cuts too.
Flossing your teeth. Use the Reach Access Flosser. Google it. Available at drug/grocery stores.