Yes! Jesus suffered not only in physical ways but also in mental and spiritual ways. We can offer anything to him, including the things you mentioned. Jesus experienced human suffering in the fullest way possible through his passion, and it was an example to us that if the Son of God was willing to go through these sufferings, and a greater good can come out of it (namely the salvation of humanity) then we will suffer as well and our sufferings have the potential to reap beautiful rewards for Christ’s kingdom. He is our perfect example, and we are called to follow him in everything.
As for anxiety and depression, I also struggle deeply with both, and something that has helped me to offer it all up to Jesus is the fact that he also went through both. The agony in the garden is a perfect example of Anxiety, he was so distraught as to what was about to happen, so anxious about it, that he sweat blood. I would argue that in that moment, Jesus felt what we call anxiety (even though he was fulfilling the Father’s will through his passion and death, he was still anxious about it!). As for depression, Jesus exemplified experiencing depression when he was on the cross and he spoke “My God, my God why hast thou forsaken me?” One could argue that he was simply quoting the old testament when he said this, and it was simply to fulfill the prophesies, but I believe he was actually feeling abandonment, that God’s light was blinded from him, and in that moment, he could not feel it. Aka, the feeling of depression! To feel so apart from God and the world despite you being in a state of grace or being out in the world! I believe that Jesus experienced both these things during his passion and when you are experiencing these pains, realize that they are valid suffering, and that you can combine your pain with that pain Jesus experienced on the Cross. He’s felt it too! I hope you take some comfort in that.
Also, Jesus experienced humiliation, and embarrassment, even just being the child of an unwed mother is enough for disgrace. He’s felt it all, and every discomfort and suffering can be offered to him. (also every good thing can be offered to him in thanks, don’t forget that aspect!)
May God bless you! I hope this helped!