Fresh piercings being cleaned properly should not be painful. They should be a bit sore at first pretty consistently throughout the day but cleaning them the right way shouldn't exacerbate it. Claires gives horrible aftercare instructions.
First off, throw away that cleanser crap you got from them. It is only going to irritate your piercings.
Second, stop rotating your piercings. Mall "piercers" advise this but actual licensed piercers will tell you that is the best way to irritate your piercings and possibly end up with an infection. Rotating your jewelry only drags dirt, bacteria and crusted lymph into your open wounds. It scrapes up the fistula of your piercing and prolongs healing.
Third, get some non-iodized sea salt and start doing sea salt soaks. Dissolve 1/4 teaspoon sea salt in 8 oz very warm water, dunk a cotton ball into the solution and hold it to your ear for about ten minutes. Do this a few times a day.
Fourth, throw away those gross stud earrings and get some proper jewelry to heal your ears with. Something made of surgical stainless steel or titanium is best. I always used to wear circular barbells and for me those were best.
Something like this is fine:
http://www.bodyartforms.com/productdetails.asp?jewelry=circular&dwzPage=2&ProductID=780&index=12
Something like this is better:
http://www.bodyartforms.com/productdetails.asp?jewelry=circular&ProductID=4014&index=13
You need 18G.
Good luck.