Altitude sickness at Neuschwanstein Castle?

No, you shouldn't have a problem at Neuschwanstein - Pike's Peak is a lot higher at over 14,000 ft. My home in Colorado is not far from Pike's Peak and I can feel a difference between the altitude around Denver and the top of Pike's Peak or Mount Evans even when I've been acclimated to the Denver area. I've never had a problem at Neuschwanstein in 5 or 6 trips there.