Rules may have changed by the time you fly in January, but currently there is a "one-bag" rule for carry-on baggage at all UK airports. This rule may be relaxed after 7th January at some airports so before your trip it's worth checking the Airport security website as well as the website of the airport from which you fly.

There is also a rule (not just in the UK but in other countries too) about taking liquids, gels and aerosols in your hand luggage. Reading this carefully should minimize any unnecessary hassle at the airpot.

Also make sure that you have your booking code as well as the e-ticket (etix) number with you. You will probably be asked for the address where you'll be staying in the US when you check-in. Make sure you have the address (street address rather than hotel name) handy.

Have a good trip