"In awe"? Are you sure you didn't look up osoreru instead? But in this case, 押す means "to keep someone under pressure", "to have the edge", etc., and 押される naturally means "to be under pressure", "to be on the defensive", etc. So your translation works; I'd just change "Am I overwhelmed" into "Am I getting overwhelmed" or something like that. Or maybe there's an even better expression... what's the opposite of "having the edge" or "the upper hand"?
I think that'd be too far away from the original intent. Keeping the series in mind (Eyeshield 21), the 'pushed' and 'put on the defensive' has meaning on multiple levels. While I don't know who the male character is I imagine he's a lineman or something.