My MacBookPro is acting strange, it was suggested i reinstall the OS. When i bought Lion it was downloaded with no disk. can i do that?

My MacBookPro, that i purchased in Sept 2009 and have upgraded many times, is now acting up. The screen is grey occationally, I cannot not leave the power plugged in or the external drive now because that leads to trouble. When i get the grey screen i get big pixels when i move the cursor over the screen and i can see my account under the grey, so i click on it and i can log in, but it has started gettng very hot sometimes, and it shuts down often when i close the lid instead of going to sleep (unless a program won't quit).

I spoke to a freind who is very good with Mac's and he told me to reinstall the OS and that should help get rid of the problems. I am at 10.8.2 and up to date on the latest OS Version. But when i purchased the last upgrade it was downloaded with no disk. Can i reinstall this OS?

Thanks,

Mary in Hollywood