Aminoethyl or ethylamine?
The IUPAC rules use "aminoethyl" for such a group. This is copied from the IUPAC "blue book" which can be found online here

Rule 811.3 - An -NH2 group, when not the principal group, is named by the prefix "amino-".

Your original name is very close to what would be used if the N were attached to the ring and the ethyl attached to the N. That would be "3-ethylamino-2-methyl. . ." according to this rule:

811.4 - Radicals RNH-, R2N-, and are named as substituted amino groups by changing "ine'' of the amine to "ino".