I also have celiac and occasionally need to travel for work or shows. When I do not have to fly, I pack a cooler of snacks similar to what has been mentioned here. Depending on the number of days I am gone, I will stop and replenish my ice in my cooler. I will also add in a few of my faves below for food that travels well.
Yogurt (I prefer low fat plain greek yogurt)
Cheese slices. I will wrap a slice of salami around a slice of cheddar for quick protein and fat.
apples, oranges, bananas and grapes all travel well
carrots, sugar snap peas, snow peas, green beans, zucchini sticks and cucumber slices will travel well. I pair those with hummus, tzatziki or any other higher protein dip.
I also make protein balls with a combo of nut butter, honey, dried fruits, whey protein isolate and GF oats.
Homemade pizza. I make a GF yeast dough for crusts, then I make up my own pizza, cool, cut, and I eat it cold. This is a pretty substantial travel meal for me.
GF tempeh. I slice it, lightly pan fry in olive oil with a bit of salt or tamari. Then toss it in a container and eat it cold. It will go with any sauce from honey to tzatziki.
Popcorn. I pop mine at home, but you can purchase store bought.
GF oreos (Because I need a cookie or four)
Things that don’t travel well in my opinion: berries (get mushy), mango pieces, delicate chips, softer lunch meats that break apart easily, frozen foods, soft cheeses or cheese spreads, candy that melts.
A couple of extras to consider packing: disposable plates, bowls, plastic ware for yourself to always ensure yours don’t get cross contaminated. A kitchen knife and kitchen towel from home in case you need to slice anything.
One other note: you mention oats containing gluten, but oats do not contain gluten. Oats are however often harvested using the same equipment that harvests wheat, barley or rye. That’s where oats can get cross contaminated with gluten. Buying GF oats (I like Bob’s Red Mill) should be safe for you. I eat a lot of overnight oats and have never had a problem as long as I only buy oats labeled GF.