Did you glue the screen in yourself or buy a service pack with the screen glued to a new frame? We advise all our customers to buy service packs through us, they are usually a bit more expensive but the finish and quality of the screen are usually top-notch.
This also stops the possibility of causing damage when setting your new screen back into its old frame.
But this sounds like a bad screen replacement to me, does the proximity sensor work when your using the phone on a call and have the phone next to your ear? It should turn the screen off to prevent your face from touching the screen.
If you had this you replaced the screen your self then I would be advising you to get a new one (Service Pack) and transfer all your parts into the new screen and frame. If it was repaired by someone else, contact them immediately to let them know of the issues, and enquire about having the screen replaced with a service pack, it will be worth the extra cost, trust me on this.
I hope this helps you get to the bottom of the screen issues :)