At any of these stores you could get a tankini. They cover up and they are comfortable to wear. I prefer them over one pieces. And you won't look like a slut! I don't think people look like sluts wearing bathing suits because it's just swim wear so you can get wet. It's not a big deal.

I can't help you and I don't see how wearing a bikini or short short swimsuit is slutty.
Buy a pair of boy's swimsuit shorts.

I don't think they even have swimming shorts that go up to your knee. Honestly if you want swimming shorts, they are going to be short because long would be too hard to swim in.

try http://worldswimwear.com
they have modest swimsuits