I’m mildly allergic to both peppers and onions, so I learned to make my own spaghetti sauce. Up until then my family had always just gotten it from a can.
I’ve never actually measured the ingredients, so the following is approximate:
1 Tbsp butter
1-2 Tbsp olive oil
2 large cloves garlic, or 3-4 small ones, depending on how small
1 heaping tbsp basil
1 heaping Tbsp oregano
1 heaping Tbsp parsley
1 large dash thyme
1 dash sage
1 pinch summer savory
1 to 1.5 pounds ground beef
2 quarts tomatoes (Diced, pureed, fresh, however you like)
1-2 tsp molasses
Optional: 1 finely-diced beet, or beet greens (or both)
Salt to taste
Peel and slice the garlic. Melt the butter in a pan with the olive oil. Saute the garlic until it just starts turning golden, then add the rest of the spices. Saute the spices all together for a minute, stirring constantly. (This recipe assumes dried spices, I’ve never made it with fresh. Depending on how my garden goes, that may change this year.)
Add the beef to the pan and brown, using your spatula to chop it into crumbles as it cooks. When browned, add tomatoes and remaining ingredients. Let simmer until thick, tasting frequently and adjusting spices as necessary.
This makes a great spaghetti or lasagna sauce. If you use pureed tomatoes and crumble the beef fine, it does well as a pizza sauce, too.
Have you tried shallots, to see if those set off your allergies too?
Onions, garlic, shallots, leeks, etc. are all pretty much in the same food category chemically, if you are good with garlic you may be good with shallots.
I bet shredded radishes might work too to mimic that onion bite... even roasted or stir fried radishes (sliced/shredded,julienne) could be a good substitute for onions. I put shredded radishes in my cole slaw instead of onions.