SH,

Is it the Bahrain- Kuwait- IAD United flight and then UA flight to LGA? If so, that flight is one of the first that arrives in the morning at IAD. Are you American, Green Card Holder or Visitor? If it is the first two options, you should have no problem getting through. The last part you should also have no problem getting through but

When you arrive, it should be gates C1- C14 and you walk in a hallway until you see a sign Washington DC or transfer. Go to the transfer point. Otherwise, you go to the Main Terminal Immigration/ customs area and would most likely miss your flight. They would have to bring your luggage from FIS to the Main Terminal, You would have to check it at the ticket counter and go through security. Meanwhile the transfer point, you get the immigration, customs, pick up luggage and drop off luggage and go through tsa security part done. When you go up the escalator, you will be at C7. UA Express flights at IAD leave from the A, C or D concourse.

If I read my handbook correctly, the BA lounge for Priority Pass doesn't open until 8 or 9 am and closes at noon or so. So I don't you will have time to take a shower there at IAD. Wait until you arrive in NY to take a shower. If possible, I would wear comfy, light clothes on the plane.

When you arrive in NY, the other posters have great advice.