This is common to most android phones.
- Press and hold the power for 10-15 seconds to soft reset your phone (this will not erase your data but it will clear any temporary software bugs).
- Make sure your hands are dry and clean when touching the screen.
- Your phone memory might be full, move some to your SD card.
If the touch screen is still slow then backup your date and hard reset your phone to factory default.
Let us know if the problem is still unresolved.