I don't think your feelings are irrational at all. Whether you are in a mono or a poly relationship, sometimes the "will I be good enough" can rear it's ugly head.
You are on the right track. Open and honest communication. Talk. Talk. Talk. Argue, if that's what it takes. Problems can arise even when we are completely honest about our feelings, but it's easier if you are both on the same page as to what you are feeling.
Going into a poly relationship can be alot to wrap your head around. Feelings you never thought you would feel are suddenly in your face, and you're trying to figure out where it came from. You don't know what your feelings will be until you face the situation, and feel the feelings. Just be honest about it. I think with time and talk, you'll know what works for you both.