Yes, your suggestion is totally right.
But I chose to drop "tuam" because Latin uses possessive adjectives less frequently than English and because it's obvious that one lives his own life, not the others' one.
Hmm. I don't think it is so obvious, dear. We sometimes live another life than ours, e.g. when we pretend being someone else...
I think the sentence even focuses on the pronoun here.
You can interpret it as follows: "live your (not others" ) life". Am I wrong?