If i restore my iphone to its factory settings, can i restore it again to its backup?

I have an iphone 5 and i recently bought an album off of itunes. I also then made a new icloud and deleted the old icloud account because of some troubles i had. After that, none of my music played so i hooked it up to itunes and then i worked perfectly except one thing: a duplicate song. This song will not let me play it nor let me delete it manually. On itunes it only shows up as one song. It always skips it. Now i have the same song on there, one works and one doesn't. I tried so many things including restoring it to its backup. I also looked up stuff on apple support and i'm not the only one. I'm considering just restoring my phone to its factory settings just to get rid of it. If i do this will i be able to restore it again to its backup?

Please help me, i'm getting really frustrated and annoyed.

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