As far as the shampoo issue. If you are staying in hotels in Europe (not hostels) you will find plenty of shampoo bottles in the rooms. Like in the US, the hotels (in MOST cases) offer small bottles in the bathroom for your use. Unless you can't live without your normal shampoo for your travels, you will have to check your bag.
With the airlines trying to make money, keep in mind you should check US Airway's website, or call. You will most likely have to pay at least $15 for the 1st check bag (per passenger)
And yes, you bag is larger than carry on size, so you will have to check. Do not think you will get away with it, the ticket agent, or the flight attendant will not let you, you most likely will have to check it at the door to the jetway, or once aboard the plane. Carry on space on airplanes is at a premium now that airlines charge for checked bags, so trying to place the bag sideways to fit is not going to happen if your plane is full!
On a side note, we've checked our bags for every trip (and yes, they were even carry on size) and NEVER had a problem at the other end (knock on wood) but it can happen that the bag gets routed elsewhere. Always check the luggage tag the agent places on your back when you check to make sure it matches your final destination, and keep your bag claim tickets with your passport or other important documents.