Welcome! I’m glad you found us, but I’m sorry you needed to.
My kids are grown now, but they both had issues with tomato products and my youngest also got marks wherever ranch dressing and toothpaste touched her. Neither one was allergic to the foods that did it. We always chalked it up to sensitive skin. It didn’t welp up or spread like hives do and didn’t itch - more like flat red hive-like areas. They each said they weren’t having any mouth or throat issues from those things. Since it was just the skin redness, we chose to keep those things in their diets. It sounds like your kiddo is having more distress from his symptoms, so until you are able to get in to the doctor, I would avoid anything with tomato ingredients. If he were more able to tell you milder and less obvious symptoms, I probably wouldn’t avoid the things like bbq sauce that might be okay, but until he can express subtle symptoms I’d avoid. I don’t think you need to get into the doctor right away, but it might be worth calling before the appointment in case they want to run bloodwork or something before the visit.
As far as what to feed him that’s inexpensive and shelf-stable, I’m afraid I’m not much help since it’s been so long since my kids were that age. Can you transition him to ranch dressing for dipping anything he’d eat with ketchup or bbq sauce? My kids really liked the Gerber meat sticks (look kinds like Vienna sausages in a baby food jar). Those were easy and shelf stable. They were pretty good veggie eaters, but always ate them better when they could dip them in something. Maybe try cheese sauce/Alfredo/ranch for dipping carrots and cucumbers in? What about hummus or sun butter - would he eat those things? Will he eat veggies that have been cooked into soup or stew - they tend to pick up the other flavors and are easier to tolerate with a picky palate. I know many canned soups are high in sodium, but if you could find some without tomato it could be an option for now until he sees the doctor. You could always add extra veggies to those, too. I’ve also heard about hiding carrots/squash/sweet potato by cooking soft and then puréeing and adding to the sauce for mac & cheese or hiding cauliflower in mashed potatoes. Roasting vegetables makes them have a different flavor that some picky eaters prefer, too. I’ve even seen things like carrot ketchup. If you can find it maybe that would work, too.
Good luck and feel free to ask questions anywhere on the board. We’re pretty laid back and won’t mind.