I go through security 2 or 3 times a week with an underwire bra and a watch and haven't set off the metal detector. I went through once with my cell phone in my pocket and didn't set off the metal detector. I believe you have to really try to set those things off.

I'm sure many other women wear underwire bras when traveling and I haven't seen a queue of women getting patted down or wanded.

You get 1 item to go overhead and 1 item to go under seat. I bring a roller bag and a backpack without issue so a purse should be fine. Just play by the rules and put it underseat if you put your other bag in the overhead. Carryon baggage requirements are enforced by the airline and not by TSA so don't expect the TSO to inform you if you have too much stuff unless you are trying to bring a 25" roller or something blatant like that.