Personally I would try the following
1. If the problem is recent and not from the time you buy your device, you should try a factory reset.
2. Apply a screen protector to see whether it helps, my Nexus 7 tablet's screen can be sticky or dry sometimes and it's also hard to touch, but after I installed a screen protector on it it's always perfect because the screen protector was chemically treated so it doesn't retain oil or fingerprints.