Short story - is it possible to have a food allergy but no hives/rash, only vomiting? And would the reaction take 2 hours or so later?

Long story - (warning: mention of vomit below)
Dd, 19mo, ate some ritz peanut butter sandwich crackers on Saturday ~2pm. At 4pm she vomited a lot, all her lunch. The lunch was not digested at all, so perhaps food poisoning? No rash or hives anywhere on her. But a while later she rubbed her eyes a lot which I attributed to her not having a good nap that day.

Saturday was not the first time she had peanut butter but definitely a larger amount of PB. Prior to Saturday she had just eaten a fingertip's worth for a few days in a row when I first introduced it to her when she was ~1 y/o.

She drank a lot of water after and vomited some water ~5pm. I gave her some banana and Cheerios for dinner but she didn't seem to have much appetite. 7pm she vomited again but a smaller amount - the banana and Cheerios.

She was also coughing a lot so it might be from her coughing too hard.

Or could she have gotten sick from the lunch we ate from a restaurant. However DS and DH had the same lunch and didn't get sick.

The pedi said it's very hard to tell what it could be (allergy, cold, food poisoning, stomach virus) but that we should wait until she's 2 y/o to introduce peanuts again so that she could communicate to us if she's feeling itchy, sick etc. I really don't want to wait that long, what if she accidentally ingests something with peanuts from now until 2. No one in our family has any known allergies.