I agree with Going Nuts, I’d start with baked eggs and something that’s baked a long time like cake and then if that’s okay something cooked not as long like cookies, etc. In general positive allergy test results are about 50% accurate, but negative test results are about 90% accurate, so I can understand why your doctor’s office advised you the way they did. What reaction have you had to eggs? That would influence my answer - and your doctor’s office should have considered your reaction history in their advice to you as well.
I am allergic to eggs, but only raw or lightly cooked eggs bother me. Baked goods are typically fine except sometimes under baked cookies or something very egg-heavy such as pound cake will make my throat itch. I also can’t do things that are all egg white - like angel food cake. I don’t eat eggs or egg dishes like breakfast casseroles or quiche, etc.