Rules for Baggage/carry-ons

I am traveling in about a month on American. I am leaving late on a
Friday night and coming back early evening on Sunday. I need dress
clothing for interviews and toiletries. I don't want to pay a baggage
fee just so I can bring my own toothpaste. If I bring an almost empty
toothpaste tube and an almost empty shampoo bottle, can I bring that in
a carry-on? What are the current rules for liquids at the security
check point? What are the current rules for carry-ons on American? I
only fly once a year to a conference that moves around each year, and I
know that the airlines have decided to steal more from customers from a
baggage fee. What other new means of making flying unpleasant do I need
to know about? Thanks.

Ken