Yes, I think it's normal. You're missing him and grieving his loss. You will probably pass through many of the stages of grief, just as if someone had died. There is no set time on how long before you are "over this." You shouldn't be expecting to get over a 3 year relationship in just a week though, so you are not unusual to still be so hurt 1 week later.

Take some time alone for yourself if that is what will help you. Or seek out friends and family for support if that would be helpful.

Hang in there.