Yes, they are both grammatically correct:
1. 'I feel as if I were a chef...' = past subjunctive
2. 'I feel as if I am a chef...' = present simple
But it depends really on what you want to say. The first one is appropriate to use if you want to state something that is contrary to fact about something that happened in the past (situation has ended), and the second one is appropriate to use when you are talking about something that is contrary to fact in the present (i.e. situation is still occurring).
Hope this helps! :)