<p>If you’re going to use like in that sentence, I would either use the contraction I’m following it or, preferably, leave it out altogether…I feel like a detective trying to solve the case.</p>
<p>On the other hand, if you’re going for something more formal, you would probably want to say, I feel as though I’m a detective. I would not use “I am” in either case. I think it sounds stilted in this situation.</p>