DD2 had a very similar reaction. I went to the hospital and I got referred to do an allergy testing.
So we saw the paed allergy Dr did the test, came up as mild allergy so they write you out an action plan. If they're anaphalactic you will learn how to use an epipen and have an anaphalactic plan. Either plan you will need for anyone looking after your child, keep on your fridge, if in Child care or going into they also will require a copy.
I wouldnt try again until after youve seen specialist. Reactions can get worse. We will go back in a year for a retest and if reaction has decreased they will do a controlled trial with actual peanuts.