You are not a horrible mom. It may feel that way today, but a lot of kids fall into this category - I had the opposite problem. My kids were both chunks, and I was so embarrassed. They've both thinned out nicely now.
Have you considered mixing whole milk with formula (1/2 and 1/2). Obviously it's not ideal and you'll need to run it by your pediatrician. But, it may make the taste of formula more palatable and give your son more calories.
Instead of baby foods, have you tried giving him table foods. Small pieces of banana, cooked frozen vegetables, small pieces of cheese, yogurt, etc?
The American Academy of Pediatrics changed their policy on what foods could be given to children at which age a little over a year ago - there are really no longer restrictions on strawberries, peanut butter, etc. unless there is either a family history of allergy or the food item poses a choking hazard.
I'd even recommend hot dogs (I know they're not really food), well-cooked noodles, turkey burgers to help with is weight gain.