Dog is super gassy and is constantly biting/scratching angrily at her butt?

I just moved in with my boyfriend recently and we've been having some serious problems with our dog Zoe. She is a rott mix. Our first problem is she has the worst horrible gas! And she does it frequently.. Like.. Eggs, corndogs and mustard.. Not the best smell of fart I must say. Our other problem is she has a nack for constantly itching her butt. Though she usually does it when shes alone or we're not constantly watching her. She knows shes not allowed to do it so she does it mostly when she gets the chance. Even when we are in bed and either about to sleep or are sleeping, she'll take the chance and bite the crap outta her butt until it bleeds all over the bed. She was eating Iams before I had switched her food to a lamb and rice Purina. After switching her food it helped amazingly after about a few months. Then it started up all over again with the bad gas and butt biting.

Do I need to change her food again? Or is this something else? What do you guys usually do to keep your dogs farts at bay?