The prayer I learned to say when the priest consecrates the Precious Blood is “My Jesus, Mercy.”
This is an old school pre-Vatican II practice. I was taught the “My Lord and my God” by my mother, and didn’t learn till I was an adult that the Precious Blood was supposed to have a different prayer. I used to just say “My Lord and My God” for both, and I think mom did too. I remember my father, who converted in 1961, always doing the strike your breast, say the prayer and bow, even when nobody else in the church was doing it. Now a lot of people do it.
I wonder why we seem to have so many different prayers for the Precious Blood though?