It can depend on the type of nut, the severity of the reaction history, and which service you want to join.
Our experience is the AF will not grant a waiver unless you can show you no longer have the allergy. Army and Navy are usually reasonable in their determinations, as in they have granted waivers for the allergy.
Type in 'Nut Allergy" in the search tool field in the upper right of the page and you will get tons of responses you can learn from
Also, ask a moderator to help you change your avatar . . . best that you don't use your real name on an open forum such as this.
Best wishes.