I just found out that I am gluten-intolerant. I have change my diet for a few months now. I feel like a different person. I have also changed the diets of 2 out of my 3 kids who have the same symptoms. They are doing better too. We finally want to change the whole family's diet 2 gluten-free. The hard part is that it seems like we have to spend more money. That's not including gluten-free baked products. How do you do shopping on a tight budget?

one thing on baked products: I have found is that as expensive as the flours are, it is cheaper to buy them and make your own baked goods than to buy pre-baked or even mixes. They certainly are handy but I can't justify to myself to buy them very often.
I buy some flours at a mennonite bulk food store, the prices are fairly cheap there (like corn flour, rice flour, potato starch, cornmeal). I buy tapioca starch at a local asian store and it's way cheaper than any health food store. You could check any Indian/Eastern market for millet, sorghum etc.
Some people say it's cheaper to buy flour in bulk online, though I haven't found it so, it may be for you depending on where you live.

Another thought is tortillas, we have a Mexican tortilleria where we can get fresh corn tortillas cheaper than what is in the grocery story.

Most things do cost more, we find it easier to just leave out certain foods altogether (dry cereal, crackers, premade cookies, pretzels, for example).