Yes, this is very much so normal.
Betta's often suffer from constipation, which is the "fat" you saw.
This also often interfers with their swimming ability and general-getting around.
A really good trick for handling this, is to get a frozen pea, and cook it so it's
mushy in some water in your microwave. (warning, this really doesnt take long at all and you dont want to over-cook the pea so it's crispy). Then, once it's done kinda squish it with your finger once it's cool enough, that way you get betta sized chucks of it. Feed this to your betta once a week rather then there regular food. It's natures natural way to keep betta's regular.
Also, if this is an often problem you find you're Betta having, you might be slightly overfeeding. With Betta's, overfeeding is as simply as feeding them too many times a day, or one more pellet then they really need at feeding time.
Anyways, best of luck with this in the future! ^_^