These concepts in linguistics are often confused, but they are quite distinct.
A phoneme is a unit of sound that differentiates one word from another. For example, the phoneme “t“ in “Tim” differentiates it from “him”. Likewise, “h” is the distinguishing phoneme in “him.”
A phone is any unit of sound in English. It need not change the meaning of a word if replaced.
An allophone is a variety of a phoneme, pronounced slightly differently to other varieties but having the same outcome and representing the same thing. For example, the letter “p” in “push” is pronounced with aspiration, more strongly than the “p” in “spit,” but these remain two versions of the same phoneme. Exchanging one for the other will not actually alter the meaning of the word.