The thing they are most strict about is the size of the bags. If yours are below "standard" carry-on max size then you should be OK, particularly if you are female and the shoulder bag looks like a handbag.

It may also depend what class you are flying and your status. Not sure if UA do this, but on CX as an Elite they will give you an orange tag to put on your carryon which indicates to the gate wardens that the airline accepts what you are carrying. The gate wardnes detach part of the ornage tag as you pass through.