Only drawbacks I've noticed to long time use (4 years): they are expensive, at least in the UK. And I think it has slightly altered the appearance of my nose (making it look puffier where the strips pull up) - but this is hard to know for sure, as I don't have pictures to compare as a baseline. I've tried to minimize any physical effect by using as small strips as possible.
H2 blockers lower your stomach's response to histamine. I believe antihistamine allergy medicines are H1 blockers: they work slightly differently but have roughly the same mechanism of action.
Amongst other side effects - antihistamines inhibit/block tanning.
Nasal strips, by contrast, are literally just holding your nose open. The worst I can imagine is that my skin might get irritated from regular contact with the adhesive, but so far that hasn't happened. They also work insanely well for me: Occasionally when I'm trying to get back to sleep, I remember that I can now take full breaths and I do it, and I IMMEDIATELY feel my brain sinking into sleep mode.
Sleep is SUPER important, and these things are all inexpensive and basically risk-free from a health perspective. (Though I would probably at least ask your doctor about reflux before deciding to take H2 blockers regularly. It's just prudent when deciding to take a new drug regularly).