Given that that this is your community's minhag, it might be more relevant to ask your community's Rav about Almond Milk.
If you read the Chashukei Chemed on Nedarim 11a, he spends a long time giving different answers why nuts are not eaten on Rosh Hashana.
חשוקי חמד נדרים דף יא עמוד א
However Rabbi YD Harfenes (in an essay in the journal ‘Ohr Yisroel’, 5756 pgs. 90-108) explains that since almonds are specifically mentioned in the Torah as שקדים and not as אגוזים there should be no reason not to eat almonds during this time.
He also says that they're not included in the general category of אגוזים.
In the same piece he talks about nuts that have been broken up and says there should be no reason to make a distinction here - they're all nuts.
I would suggest though, that based on the logic above, since milk derived from nuts is no longer the same min - i.e. it is no longer a nut, but a mashke - a drink which has a certain percentage of water and thus has a different name entirely - milk and not nut; I would venture that this should also not be included in Egozim. However, since this is dependent upon one's community's minhag, you should be asking your community's Rav about whether nut-derived milk is included.