As far as I know, a serious reaction would show up immediately, like rash around the mouth or on the hands, or in the very rare extreme case, swelling, hives - a severe allergic reaction.
Usually when you lo is just having trouble with a new food, you'd get lots of gas, change in poop behavior (such as constipation or diarrhea), crankiness and NW's with abdominal discomfort. Often these foods can be re-introduced at a later date, when their system is more mature. For example, my lo got very constipated on rice cereal (which is very common) so we switched to oat or barley. She also had trouble with pears and got a tummy ache at night (lots of NW's and crying). We held off the pears for a while and tried them in a couple of weeks, then she was fine.