I have always teared up fairly easily. Only recently have I learned why. I usually tear up during mass. Sometimes even the readings will cause them to flow. The consecration is another point, but after receiving our Lord in the Holy Eucharist, I generally cannot stem the flow of tears, and no longer desire to. Those who stood at the foot of the cross shed them without shame, and that is precisely where we are at mass. But, they can be tears of sorrow or of gratitude - or both.
We are correct to sense sorrow, regret, shame or guilt during the mass, as it is our sins that betrayed the Lord, that abused Him, that crowned Him with thorns, that nailed Him to the cross. These sensations are intended to provoke a spirit of repentance within us. Yet, these are not condemnations of the Lord, but rather calls to that same repentance. Yet, these sensations that we experience must be in proportion and appropriate to the situation. If they become extreme, it might be time to speak with Father about them.
In any event, I would Seek out a priest who is knowledgeable regarding the gifts of the Holy Spirit, and their fruits in our faith life. A conversation with him might settle any anxiety you may have regarding these manifestations. But, at the same time, if you are moving closer to our Lord, beware the evil one. He hates that, and may set some snares to trap you. I find that he lies in wait right outside of the confessional.