9 month old son has tantrums at nap time with mom.?

My 9 month old son has begun throwing tantrums when I finish reading him stories at nap time. I believe it's because he wants to nurse some more because he does not act this way with his dad. He has had issues with reflux and has fussed while nursing since he was 3 weeks old. He doesn't seem to have many issues anymore, but will only nurse for about 5 minutes at a time. I don't know if he's getting enough milk sometimes, so I'll let him nurse again when he's more sleepy. He then proceeds to fall asleep and when he wakes up, he becomes very upset. I continue with the nap routine and as soon as I try to sing lullabies, he is screaming and climbing up me. I know part of the problem is because he's over tired. I thought I might offer him water instead of the additional milk. Anyone have another suggestion? BTW he also wakes in the middle of every nap and has trouble falling back to sleep without my help.