Why do people always bitch at the OP of medical advice threads to go to the ED, urgent care or their PCP immediately, depending on the interpreted severity-level of the presumed or hypothetical diagnosis? It's well established we have several physicians, at least two doctorally-prepared family nurse practitioners (I am one of them; the PhD, FNP, not the DNP, FNP & PMHNP. And neither of us, I don't think, are the NP who used to post here, and who spent numerous years working on military bases overseas before returning to the U.S. to work at, as he called it, like it's still 1952, "a VD clinic." I'm pretty sure that wasn't me. I can't say for sure about the psych DNP), possibly at least one physician assistant (who, I recall, had to resign following brain surgery, if s/he still posts here) and countless RNs and other medical professionals who post on DL. Unless there is a high probability the person is having an MI (heart attack), CVA (stroke) or similar subarachnoid hemorrhage or subdural hematoma, experiencing an opioid or benzo overdose, in acute renal or hepatic failure, experiencing symptoms of potentially life-threatening inflammatory/infectious processes like peritonitis or epiglottitis, in anaphylaxis or an anaphylactoid reaction, or septicemia/in septic shock, etc., what's the harm in seeking advice on a message board? Even if you took the cynical view that all of us medical professionals are lying about our education and credentials, there's still a good chance a fellow poster will have gone through the same, or similar, and can offer sound advice based on experience and/or their medical provider's treatment and recommendations.
OP: Slather it with butter, of course! Just kidding, definitely don't do that. You have received pretty good advice thus far, so I don't really have much new to add. I see you're allergic to sulfonamides, Neosporin/bacitracin, penicillins & fluoroquinolones, so that limits your options, especially for OTC topical antibiotic ointment. For cutaneous burns, silver sulfadiazine 1% topical and silver-impregnated dressings are first-line treatment, as well as mafenide 11.2% topical (Sulfamylon, Rx-only), but you can't use them, except some types of silver dressings. If you can get a silver-impregnated dressing that isn't sulfadiazine, like 1.4% silver alginate pads (silver calcium alginate) or silver nanocrystalline, you should be okay to use that. Likewise topical silver nitrate gel. I'm not sure if CVS and the like carries them, but if you can find Smith+Nephew Acticoat 7, they're a good nanocrystalline silver option, but likely quite pricey. Alternatively, the previously recommended hydrogel burn pads are another good option. And, of course, keep the wound area clean with good ol' lukewarm tap water and a mild soap or an antiseptic like benzalkonium chloride 0.13% (avoid Hibiclens and Betadine). 3M Wound Cleanser is another good choice. As you mentioned already using, topical lidocaine cream is good for temporary pain relief; benzocaine 20% is another. If you apply the lidocaine and then cover it with an occlusive dressing such as 3M Tegaderm for about an hour, it will increase absorption & be more efficacious.
Assuming you're not allergic to them as you are to seemingly everything else under the sun (just kidding), and they're not otherwise contraindicated for you for other reasons, then oral NSAIDs like ibuprofen (Advil/Motrin) or naproxen (Aleve) can be used for pain relief. If you are allergic to NSAIDs or they're contraindicated, then, of course, acetaminophen/APAP (Tylenol) can be used, but doubtful it would help much. If you're lucky enough to have some leftover, or an active prescription for, Vicodin/Norco, Percocet/Endocet/Primlev, Dilaudid, Roxicodone, M.S.I.R., etc., then even better. An opioid/opiate would provide you real analgesia, but good luck trying to get a script for one these days. The moral of the story is: keep it clean & covered, even if only with a simple gauze wrap to protect the wound from trauma and dirt, and you should be okay. Hope you feel better soon!