Whenever I use the paddle shifters while driving, switching gears is very slow.

Ex. I’m in first gear (redline at 6.3k) and I shift up at around 5.5k and the car takes a second and a half to actually switch the gears.

Is this normal for a car of this age or should i go get it checked out?

First gear on anything with an M157 is over in the blink of the proverbial eye. If you are waiting until you see 5.5k on the tach to shift out of first, that's way too late. Either grab the paddle as it swings past 4k, or use Sport mode. Otherwise you will meet Mr Rev Limiter. Ask me know I know :-).

To see if I am right - does it take a long time to shift in the higher gears ?

Trying to get max acceleration times in the lower gears takes some practice. Second is over really quick as well.