can't find icons for apps on my iphone yet if search for them they are . Help

So I just synced my IPhone 4S with my computer and shared the account with some other family ones. So i go back to my iphone and find a problem. Some of the apps that were there are gone and yet if I go to the search box and lookup the app I can find it and use it. I also can't rebuy the app because it says I already own it in the App Store. Why can't I find the app icon in my iphone? HELP??