Itchy in itself does not mean bed bugs. You could just have a dermatological reaction to the sheets or the detergent used to launder them.
Do you have actual bites? They will be small red blots on our skin.
Check underneath the sheets. If you see red stains on the mattress, you might have them. Check behind the headboard. They like to hang out there during the day. They like to hang out anywhere during the day where it's dark.
If you do have them.....chances are they have gotten on your clothes and in your luggage. You could definitely try laundering everything before you leave in hot water, however, they still may be in your luggage.
When you get home, leave your luggage outside. Take all of your clothes out of the luggage and take it directly to the washing machine. Wash everything in hot water. (This includes the clothes you're wearing.) Then, you want to wash/clean the luggage. Still leave it outside. Sadly, most insecticides sold to the public won't kill bedbugs. There's a good chance you'll have to throw the luggage away. You could check with a professional cleaner to see if they could help if the luggage was expensive.