One of our cats had the sneezies - she was definitely lethargic and under the weather and was sneezing a lot for about a week, stinky snot flying everywhere, and I think a bit of a temperature. I decided that, since she was still eating & drinking OK, I'd let her try to fight it off herself. For about a week I took her to bed with me every night to keep her warm & cuddled. She fought off the infection with no problems. I did a lot of reading up on the internet & came to the conclusion that "wait & see" was the best policy (it could just be a grass seed up the nose). In general, both for pets and for family, I prefer to try to let things take their course rather than intervening with antibiotics etc.
If she had stopped eating, peeing & shitting then I'd have taken her to the vet.
If it runs into weeks then its probably worth going to the vet in case its a chronic thing that is going to need ongoing treatment.