Is it possible to have post-partum three years after childbirth? or is it just plain depression?

Yes, this is depress: Althought the stress of children continues, at three years of age you should be able to adapt to being a mother and the demands of raising a child. Symptoms this late would be treated as depresion.

Depression: I think at this point it is depression. You need to talk to your doctor and family. You may need medication and therapy.