Building immunity and gut health back after taking antibiotics

I caught whatever horrible flu is doing the rounds atm, which then turned into a sinus infection. Doc has given me antibiotics as a last resort (hoping it’s bacterial) because I can’t seem to kick it. Annoyingly this is my third round of antibiotics in the past year or so. Prior to that I hadn’t taken any in several years but due to chronic stress I’ve had a few health issues this year. As someone who has always had a sensitive gut, I’m worried that this is going to set me back even more. Any tips for building immunity and gut health would be greatly appreciated. Thanks!