The reason you have cyno:
1. Not enough water flow
2. Nitrates/nutrients in your water.
Please test your water for Nitrates...
Chemiclean is only a bandaid. This is a temporary fix only. Siphon it out and do some water changes(I think that using chemiclean requires a water change afterwards anyway). My guess is that, like you said, your skimmer isn't big/efficient enough and you have too many nutrients in your water.
Types of filtration:
biological(live rock, bioballs), mechanical(your T-shirt, filter media), chemical (activated carbon)
Pouring water through a shirt is only mechanically cleaning the water.
You need to get out the Nitrates...this is done through water changes.
Hope this helps....