Can I take antibiotics for sinusitis after one week of having the COVID vaccine?

Hi doctor,

I have recurring sinus infections, probably four or five per year on average. I had my COVID vaccine before one week and was sick for two to three days, but after that, I started having sinus pressure that was causing pain in my teeth. I went to the dentist to rule out an abscess. Today I went to a walk-in clinic, and they prescribed me the antibiotic tablet Cephalexin 500 mg. When looking up information about this antibiotic, I noticed that it had a list of several vaccines that I should not take with this antibiotic. I called the pharmacy to ask them if they thought it would be a problem to take it, and they said that it could make me sick and contact my physician to be sure. Unfortunately, there are no physicians in the area available. I am trying to figure out if the antibiotic is worth the risk of getting sick and what kind of sickness that might entail. Please note that the sinus infection is moderate to severe. I am telling you this, with the pressure it is causing on my teeth roots and a small blood clot that came up while clearing my sinuses.