Chest pains, achy arms and shoulders and bad headaches all at once for the past 3 days (at the same time each day), can this be from lack of sleep?

Yes: And many other reasons like stress, poor posture at work or school and caffeine withdrawal. If this lasts and becomes an issue see a pain physician for a good history and physical exam.

Possibly : Lack of sleep can account for a lot of symptoms . If you know you are sleep deprived try your best to get more sleep. Of symptoms do not improve then seek help.