How many carry-ons per person on an airplane?

First of all you need to check the website of the actual airline you're flying with; the TSA doesn't dictate the baggage allowance, the airlines themselves do.

Second, again, check with your airline for specific size requirements. All airlines that I know off allow one carry-on and one personal item per passenger, so you should be good on that, but the size allowances do vary somewhat. The carry-on can be bigger than the personal item and must be stored in the overhead compartment; the personal item is smaller and goes under the seat in front of you.

Yes, the luggage guidelines are per person so you get your one carry on and one personal item and your brother gets his one carry on and one personal item.

You can also combine items, if possible- for instance, you could stick your purse and camera bag in a small backpack and carry both of those items on and/or he could put his laptop in a backpack and have other items with it, as well.

One check in baggage, one carry-on baggage a laptop with or without case and a camera is allowed for one passenger.

The carry-on arrangements you have fit the rules perfectly. Have a good flight.