Actually, there may be an exception (depending on the airline), since OP is carrying photo equipment.

This is from the TSA website:

"You may carry one (1) bag of photographic equipment in addition to one (1) carry-on and one (1) personal item through the screening checkpoint. The additional bag must conform to your air carrier's carry-on restrictions for size and weight. Please confirm your air carrier's restrictions prior to arriving at the airport."

"Air carriers may or may not allow the additional carry-on item on their aircraft. Please check with your air carrier prior to arriving at the airport."

I raised this issue with AA (just through their e-mail comments, not going any higher) and they seemed oblivious to the third-bag exception and quoted me the standard two carry-on info. I'd be curious if anyone has any success in doing this with any carrier.

I usually carry photo equipment, as well, and even though it's well-insured, it's not something you want to check.