Job’s expression of grief was itself an act of worship. It doesn’t say that he grieved, and worshiped and then got over it.
To grieve as a Christian is an act of worship because it is a statement of faith that one day things won’t be this way. It’s a Romans 8 cry for Jesus to come back. Underneath your grief is a tune or song that cries out “MARANATHA! – come put things back the way they were supposed to be!”
Underneath our grief is a cry for that day when we will enjoy sinless hearts and minds and disease free bodies. That’s why you don’t need to be ashamed of grief.