I do it but it sure is difficult. I'm also low income and there is no financial aid unless we pay income tax, save receipts for gf foods and get a deduction. I've signed up at the local food bank but have to give most of the foods back tho I have gotten some dry beans and frozen pork roast I could use, bag of potatoes and occasional produce, tomatoes, strawberries, a 2 lb bag of frozen blueberries.
They usually have a variety of canned veges and fruits which you might be able to tolerate.
I look for sales on meat, cook thoroughly then cut up and freeze. Winter squash is nutritious and has carbs as do carrots which keep well. Other root vegetables are nutritious. The people at the food bank often save gf foods for my bag. I use the 'legal' food list at the Specific Carbohydrate Diet to guide my diet.
Have you thought of finding other nearby Celiacs or gf people and cooperating on food buying?