Hi Jade. My answer to your questions is definitely ‘no’. It is not wrong. Some people are really strict about this and will tell you that you are not playing the ukulele correctly, but I am more a supporter of whatever feels good for you. If it allows you to strum smoothly, than why not go on?
It is however quite fun to try different ways to strum, for example try ‘slapping’ and muting the strings while you are strumming. I generally change the way I strum according to the song 🙂
Good luck and keep enjoying to play the ukulele!