Kids clothes can be very expensive, i used to work at Gymboree so I know.
But you should check walmart, k-mart or any of the big department stores. Here in Canada we have sears, and the Sears outlet stores are very good. So yeah, if there are outlets or warehouse sales near your area, check them out. They are very good. Also, if you are a regular mall goer, check out the kids stores. They have really good clearance sales and they are amazing. When I worked at Gymboree, a dress would cost $36 when we first get them...and in a month or two, go down to to about 12$. Check them out and I am sure you will find LOADS of things that fit your budget.
I think that you will find what you want at either plndr.com or jackthreads.com, they offer a lot of indie designer brands of tees. There are more sites that have daily designer sales listings but they typically do not run as many tees sales; you can find a complete list of sales at estylesonline.com, they list all daily sales.