I didn't have neulasta. I did have nupogen and that did upset me. It made my bones ache terribly, I got cramps in my feet, and felt pretty misereable. It worked though and brought my blood counts back into sync.
I don't want to scare you, but you should consult with your doctor just to rule out some sort of bleeding. If his blood is very thin, he could be leaking some blood through the veins and the doctors want you to watch for that during chemo.
Low blood pressure can make one feel dizzy and tired. If you are concerned, sneak away and give the doctor a call. It will reassure you and that is what they get paid for. My husband often sneaked out in the garage and called my doctors. After it was all over my surgeon calls him my "mother hen". They understand. Best wishes and prayers.