Bad mood swings and bad depression after my dog passes away is that normal?

Very normal: It is normal to have that sort of reaction from such a traumatic event. It takes time to grieve and people do it in different ways.

Yes: The death of a dearly loved companion can certainly provoke depressive sx. Look for a support group, seek out individual counseling. Funeral homes often know of support groups. Talk with a trusted friend or religious leader-for support or advise for groups.

Grieving: I am sorry for your loss. Yes, loss of a friend and family member such as your dog can lead to grief reactions. See: https://www.rainbowsbridge.com/Grief_Support_Center/Grief_Support_Home.htm