I dont think it is anxiety. If he just started school and it started when he went to school it is a change. Try putting him to bed a little later. If he wakes go in rub his head or back kiss his head and walk out, make sure lights are very dim, my kids will wake up if the lights are on in the other room. He is probally just trying to adjust to the change of going to school. How does he do in school is he making friends well
You're probably correct in your assumption - separation anxiety. But this does not mean it is separation anxiety disorder. You should be able to find more information on this topic by googling "separation anxiety" or "anxiety in children" or "school anxiety" where there should be listed some interventions and ideas to help your son. By the way, if anxiety is the issue, it will not be a "phase" but your son can learn how to manage his fears and anxieties. If it would make you feel more comfortable, bring up this topic the next time you visit your gynecologist or family doctor for more advice. However, if anxiety is the issue, your son's anxiety will not be "solved" in days or weeks - probably more like months or years. Sorry - but even though anxiety is highly treatable, it does take time for the child to learn how to cope and manage. I wish you the best ....