no need 2 give up. it's like that in the very beginning. my case is similar to yours. now, my bb is going 2 be 5 weeks and i can at most pump 2.5 oz on 1 side while i am feeding her. this is most effective because i pump less if i pump 2 sides at the same time. i am not a rich mom 2 and i am always worry about my supply. but just try our best and relax.
last but not least, in fact, bb takes more in breast feeding.