Swan's Practical English Usage has this to say on the matter:
However [as opposed to Present Perfect], present and past tenses are occasionally found, especially in sentences about changes.
‘Since last Saturday I can’t stop thinking about you.’
‘You’re looking much better since your operation’
To me personally, using Simple Present emphasizes the causal link between current state and a past event, while Present Perfect is more about establishing the time at which it started.
So your sentence is correct, although note that since here is not fully interchangeable with because - a sentence like:
I'm not myself because I stopped smoking.
does not imply that you not being yourself started right when you gave up smoking, while using since in this context does.