If you are shooting one handed you are maintaining a firm grip on the pistol. How much it recoils up depends on your strength - some people's firm grip is less strong than someone else's.
If you are shooting two handed, certainly your grip is even stronger. If you look at any IPSC shooters in videos you will see minimal muzzle rise.
As pointed out, shooting left is a common trigger problem for a right handed shooter - pushing the trigger slightly. However, you haven't said whether or not you are shooting an adjustable sighted handgun, or fixed sights. If adjustable, and you are always shooting left, adjust sights. Non-adjustable, confirm your technique and then decide what to do with the sights.