Hi. I live in Rock Hill. I've never used the public facilities but thought I would help. You should probably check out:
http://www.cityofrockhill.com/prt/pools.asp (broken link)
Also, there is a YMCA facility:
http://www.upymca.org/branches/aquatics_center/AC-branches.html (broken link)
As for Carowinds, their regular pricing info is at:
http://www3.paramountparks.com/carow..._admission.cfm
But, you might want to do a search and see if your eligible for any discounts (Bilo has one, maybe AAA):
http://www.google.com/search?hl=en&q=carowinds+discount
Hope this helps!