I'm not a dr no but I am in healthcare, don't want to give any more detail than that.
The gut is literally the center of everything for us, including our immune system, hormone manufacturing, nutrient absorption etc. The best way to improve gut health is by cutting foods out that are proven to be damaging - grains and cereals. They're damaging to the gut, they're endocrine disruptions (most of us don't have thyroid problems for example, we have autoimmune thyroid damage that is caused by gut issues) they're also damaging to our brain.
If you've had antibiotics then I recommend at least 6 months of probiotics. Probiotics are fine if you have a good balance of bacteria. It feeds the bacteria in the gut but if you've got an imbalance of bad over good then you're continuing to feed the bad bacteria.
Personally I use and recommend Bio-Kult. I'm not affiliated with them but I've found them to be most effective. Some brands don't protect the bacteria from stomach acid so they're killed off. I also eat fermented food like kimchi and drink kefir to keep things balanced.
Protect your gut by avoiding antibacterial household products including hand wash, shower gel (we have and need a skin microbiome), household cleaners. You will absorb it either through the skin or by inhalation.
I've worked with thousands of people with everything from ADHD, depression, anxiety, Crohn's, colitis, diverticular disease, eczema, psoriasis, asthma and more and fixing the gut has breathtaking results on these ailments!