If you are using art from a site that offers them as a free to use license then it doesn't matter if that art is used by others as it is free to use and can't be copyrighted by the ones using it. But I recommend to try to get a hold of original art instead if you can't make it yourself as it automatically makes a game less interesting and unique if the same characters is seen on other games around the stores.
But if you have no budget then you can use free to use assets without having to worry about copyright issues. But make sure they are offered from trusted sites and if you can use it without limitations even for commercial projects. And also see if you have to credit the artist or not.
But read the license information on the assets you want to use. It tells you what you can and can't do with the assets.