It is very possible for you to be negative for Celiac and still have a gluten/wheat issue. One of my friends gets incredibly ill from eating wheat, but she’s negative for Celiac.
Gluten free = no wheat, rye or barley (and only certified gluten free oats).
You can have potatoes, corn, rice, etc; pretty much any other grain is OK.
Most processed food either contains wheat or it is manufactured in shared facilities with wheat, so I can’t eat it. You can get specialty gluten free foods – breads, cookies, pizza crusts, frozen meals, etc. but they will be expensive. Because of these two issues, I make nearly all of my own food from scratch. I eat a lot of fresh meats and grilled vegetables. Besides that, I can a lot of pan-asian food (chinese, japanese, thai, indian, etc). Lots of sushi and curries in particular. The only tricky thing is that I have to use gluten free soy sauce (San-J) is best. You can also eat a lot of corn-based Mexican food. Before I went gluten free, my diet was more pasta based.
Do you have a Trader Joe’s anywhere near you? TJ’s isn’t very expensive, and they are terrific at labeling their food as Girlfriend. They are also the only manufacturer that cleans their equipment well enough that I can eat products made in shared facilities with wheat and not get sick. Most grocers have a gluten free aisle, though. Whole Foods has a nice gluten free selection, but again – they are expensive.
You need to stop cooking with wood. Wood can absorb gluten. Cast iron cookware and cooking stones are also dangerous. If you want to try the elimination diet, you really need to try it full force. It’s very easy to introduce wheat somewhere unexpected. Luckily, there are lots of good resources online. Just do some searching. This should be a nice start, though.
Also — there aren’t really any meds you can take for gluten. Yes, some people use GlutenEase or things like that, but it’s a cover up. It isn’t like lactose intolerance where you lack an enzyme and taking a tablet with that enzyme will solve the problem. You may be dealing with an immune reaction. An elimination diet is your best bet. Besides that, there’s always medical marijuana (which does have an modulatory effect on the immune system). I haven’t tried it, but I know some people who swear it works wonders for them.