What would you do?

Just looking for a little advice on what you would do in this situation. My little boy had a reaction to wheat when we first started weaning, his gp referred him for an allergy test which came back allergic to egg and wheat. Fast forward to beginning of December he had a second allergy test. Egg is the biggest hive and wheat is a lot smaller than his first test, his first test the hive for wheat was 12mm and egg was 11mm. Before he had the test we seen a doctor and she basically said ‘he’s not allergic to egg it’s just because he has eczema’ and that if the reaction to egg came back smaller than 6mm then we would be told to just go home and introduce egg to him (which obviously we are not going to do looking at the size of that hive). The nurse that done the test said wait for a letter and we will decide whether he comes into hospital to try wheat again but in my mind I’m like how long could that take, am I better off just reintroducing it my self? And why if the reaction to egg was smaller was I told I could just go home and introduce but different for wheat? Basically I’m just wondering whether you would reintroduce at home or would you wait for the hospital to be in touch? Thank you! X