A misconception about grief that many people have had (including myself in the past) is that grief is not godly. When you first receive bad news, there is grief. I know for me, when I first heard that Trenton might have problems, I was frozen in fear, and I just needed a chance to pray and talk to God about it. Fear is not godly, but it is all about how you handle the fear. Seeking God and casting your cares and anxieties on Him is the right way to handle fear that comes with grief.
Some might feel that their grief is a private thing, and that is fine, but do not let it be private because you think it is a lack of faith or trust in God. It can become that, but grief itself is something that God understands. Christ grieved for his friend Lazarus even though He knew that He would be raising him from the dead. His grief may have been for the family of Lazarus as well, but he nonetheless grieved while trusting His Father and knowing that He would soon be making all well again. He grieved with hope. He grieved for His own pain, suffering, and separation prior to the cross while knowing that soon He would rise again and be with His Father. It is not ungodly to grieve. It is possible to hope in the grief.
I Thessalonians 4:13-14 discusses how we should think about the grief associated with the death of those we love, but it can be applied to all other types of grief:
"But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope. For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with Him."
Grieving like a Christ means grieving with hope. We have the hope, that because Christ rose, our loved ones who were saved will also rise again and have new bodies. We have hope that no matter how much pain and suffering we have on earth, all will be well for eternity in heaven
We all have moments in our grief that might not look godly. We might ask "why" and question God and His plan. Those thoughts are normal fleshly responses to trials. God forgives us for these thoughts when we turn to Him in faith and hope. We may have to ask forgiveness over and over, but what matters is that we always return to the hope that we have in Him.
When you are grieving, you do not need to paste on a smile and say you are fine. It's okay to grieve. It's okay to share your struggles and how God is helping you. That is not ungodly. This response will likely draw those who have no hope to desire what you have.