No, they do not damage your hair. They're called protective sprays for just that, to protect your hair. The only spray that's bad is aerosol, cause it's bad for the ozone lol. Generally you don't need to use a thermal protective spray before you blow dry. You want to use an anti-frizz spritz or something of the like. Before you put anything hot on your hair, like a curling or flat iron, that's when you want to use the thermal spray. Pretty much any kind of spray you can buy at a beauty supply store is good, but the best would be Something by Farouk, bio-silk is fantastic, Regis products are good, the TIGI line is good, my wife says she isn't crazy about Paul Mitchell products, but some people we know like it.
With any thermal spray, if you use too much your hair can look greasy, like you haven't washed it in a week, so she says to spray a few pumps, or put a pea sized amount of liquid in your hand and run it thru your hair as evenly as you can. If you use hair spray, make sure it isn't the kind that gets real hard and stiff. My wife uses Aussie Max Hold. It hold her hair for a long time, and her hair moves like she didn't even use any hair spray.
If you're worried about frizz, get a hair dryer that has an ionizer on it. It keeps your hair from drying out and frizzing. THAT'S what hurts hair when it's blown dry, the heat reacts with the chemistry of your hair, therefore taking out what keeps your hair from frizzing. Kind of like static electricity. If you have an ionizer on the end of the dryer, then it prevents certain chemicals from leaving your hair as it dries, leaving it less frizzy.