Hi Joshsmom, I haven't flown United in decades, but regardless of the airline, you should carry documentation for the Epipens and Benadryl, particularly if it is the liquid. And if possible, carry the Epipens in the original packaging, with the prescription label.
Truth be told, we haven't had a problem with the Epipens in years, but you never know. And the last thing you want is to get to security and have them give you a problem.
Have a great trip!