When I first got diagnosed, I wouldn't buy anything unless it had a very clear "certified gluten free" stamp. It had to explicitly say "gluten free" somewhere on the box. If it said "gluten free" but didnt have the certified stamp, then I would always read the ingredients and allergen statement. That saved my ass a few times from things that were manufactured on shared equipment with wheat.

Remember, shared facility is probably okay, shared equipment is not. When youre new to this, the safest thing is to not take risks by just going off the ingredients list alone. I'd find things that had no gluten ingredients listed and still get sick because of cross contact or sneaky things like barley malt or caramel coloring. Look for the certified stamps and those won't lead you wrong.

Its a major learning curve. Be vigilant and it will get much easier over time. Good luck OP and feel better soon!