Omicron symptoms are very, very similar to common cold symptoms. I'm on day 5 of covid and my symptoms are very much cold like for me - Runny nose, congestion, sneezing, headache, but no cough.
Apparently at the moment about half of people with cold symptoms actually have covid. So could be either, but if the rest of your household has covid, it would be an unlucky coincidence for you to have some other cold at the same time.
I'm triple vaccinated and was stuck inside with my covid positive kids for a week before I got it (they were mostly asymptomatic, certainly none of them suffered any of the 3 official covid symptoms). During that week I felt a bit rough, under the weather, just like you do when you've got a cold brewing (except it went on for longer). I was testing negative daily on LFDs and even had a negative PCR.
One of my gf's kids also caught covid last week (not from us). His sibling (and they share a bedroom) now has a cough as well, but is still getting negative LFD results. And because his cough isn't 'continuous' they've decided not to get a PCR. I know I would be in those circumstances, it can only be a matter of time.