Hey there! I hope you’re doing well and staying safe and healthy! As others have said, incense definitely isn’t essential in magickal workings — I’ve maybe used it in my practice maybe a total of 4 or 5 times, and when I did, I used palo santo (make sure it’s ethically sourced!!) and frankincense resin.
I avoid most incense since (1) I, too, have allergies and asthma, and (2) I feel like most store-bought incense has too much artificial crap in it, and if I’m going to be exposing myself to smoke, I want it to be as natural and “healthy” as possible.
While I’m on the topic of burning resins and other herbs, I wouldn’t recommend it if your respiratory problems are any worse than my asthma, but I would think that burning herbs would be at least more natural than most incense, if that counts for anything.
HOWEVER, please be careful which herbs you burn and who you burn them around, as not all herbs are safe to breathe in as smoke, and TRIGGER / CONTENT WARNING: pregnancy safety warning follows some herbs are not safe around those who are nursing, pregnant, or trying to get pregnant, as they can cause harm to unborn babies and potentially even induce miscarriages. However, I’m no expert, so I’d suggest doing your own research to make sure you’re making healthy choices that fit with your individual needs and beliefs.
Essential oil diffusers are a great alternative as others have suggested, at least from my experience. The smell is much more mild and much less obtrusive, and you’re not breathing in smoke. Please keep in mind, however, that some essential oils should not be used around pets and young children.
TLDR: Incense is not necessary, and there are other alternatives, but please always do research to ensure you’re staying safe and healthy