I think this is very tough; I certainly could not have come up with so good an answer so quickly, Jon.
The main criticism I might have is that your version (which for the benefit of the OP I will explain means literally "It is not who I am but my deeds that...") loses the effect of the two parallel clauses in the OP's English ("...not who I am but what I do...").
It seems to very difficult to use "who I am" as a subject in Latin as we do in English, and if we do, surely the verb should be singular and first person? We slur over this sort of thing in English, but are more careful in Latin (Agnus Dei, qui tollis (not tollit) peccata mundi...).
Yet for your "deeds" of course we would want plural and third person.
We might perhaps resolve the difficulty by the nominal use of the two infinitives:
Agere haud esse describit me.
Usually infinitives are so used mostly with copulae, but there are exceptions, and this "feels" OK to me (for whatever that's worth).
Can we add meum, either just before the agere or before both infinitives? I am not willing to stretch matters so far; I can't say exactly what would be wrong with doing so, but it doesn't sound idiomatic to me. I would happily accept such a usage if anybody can find a similar phrase in an authoritative source.
I might have succumbed to the temptation to use definito (especially with so little time to work). But I agree that your describo is better.
Bottom line? My recommendation is
Agere haud esse describit me
which for the benefit of the OP I will explain means (more or less) "It is doing, not being, that defines me". What do you think of that Chazzer? Jon? Others?