White worms are planaria and alot of times result from having excess food in/on the substrate. Gravel vaccing helps alot with that but if the tank is planted that makes it a little more difficult. Bare bottom you'll probably never see them again unless it gets NASTY.
The cloudy white is probably just a bacterial imbalance... if the tank hadn't been changed in a while OR is still fairly new (under 4-5 months i'd say) then the water changes may have killed some of the filter bacteria.. the bloom is from the remaining bacteria multiplying like crazy to eat all of the food (in this case probably ammonia). If you cleaned it 100% to remove gravel then that would be the cause. The gravel holds alot of that bacteria... as do the filters. That sponge should hold quite a bit. Never had good luck with Bio-Wheels maintaining good bacteria long term... so I wouldn't expect much from them.
It'd be a good idea to get the water tested to really know. Most local pet stores will test water for free, and any chains should.. call ahead to be sure. They might just be able to sell you a seachem tester, but it probably isn't 100% necessary. If the tank was cleaned out completely then you're going through another cycle..
Personally I would let it go and see if ammonia/nitrite spikes too high.. keep an eye on the fish.. see if cycle rebounds and water clears up and levels rebalance... if not, fish may be in for a bumpy ride.. may want to get a bacterial product like Cycle or one of the other brands to try and get it going again in that case.