Go to your Monitor Settings windows, where you can find the current refresh-rate settings. Make sure it is on 60Hz. New monitors sometimes come on low settings just for compatibility and need setting up. While your here adjust your brightness settings etc.
If it is already on 60Hz check your graphics card settings are on 60Hz.
Finally load up TF2, open up console commands in-game and type "cl_showfps 2" to see your current fps in game.
e.g. Monitor = 60Hz, Graphics card = 60Hz, TF2 = 75fps then your monitor is definitely running at 60fps.
Hope this helps
P.S. if this is a much better monitor than your old one the on-screen video does seem weird due to the increased clarity. Can take some getting used to.