If your tank is cycled, then your water change somehow upset your biological filter, and the cloudiness is the only time you actually can "see" the bacteria. They are multipying like crazy right now to catch up to the ammonia supply in your water. This happens sometimes when you add water back into your tank that has not already been pre-mixed with dechlor. I get that quite frequently with my 10 gal. tank. I use a python, and add the dechlor to the stream as it is going back into the tank. The cloudiness should disappear within a day or 2, and your water will be crystal clear. If you do another water change while the water is cloudy, it will stay cloudy until you let it balance back out.
Now if your water is cloudy green, which it would have been like that before you did your water change, that would be free floating algae causing the cloudiness. I'm assuming though that your tank looks foggy with no greenish tint, right?
Look at the green water algae pictures and tell me if that is what it looks like.
I would just leave it alone for a few days unless you are sure it's algae. I've never had that problem, but I will find you an answer if it is. I think one of the ways you can eliminate green floating algae is with a UV sterilizer. That can get pricey, and then you have other issues you will need to address if you go this route, so let's just take it slowly and see if the tank clears up on its own. It's not hurting the fish when it's cloudy unless it's got high ammonia. Did you check your ammonia and nitrites yet?
Hey Gunnie...thanks for the great website! I'm going to look for a siamese algae eater right away. My o-cats don't quite do the job. I have the little bright green dots of algae all over my glass and I can't scrub it off by hand. That stuff is tough. So now I know which type of algae eater will eat it. Thanks!