I would ask the priest when you can get your medal blessed. Leave it to him to decide.
I’ve had 3 very different experieces with blessings. The first in my old church, the priest was done with mass, I was leaving (last one out) and asked him if he could bless my rosary. He seemed “put out” I think he sighed, did a sign of the cross over it, said a few words and gave it back.
The second was buying a rosary for a friend in a church gift shop. The priest put holy water on it and said a few words before I paid for it.
The third experience was in my new Dominican church. The friar told me to meet him in the sacristy after mass, he put things away and then did a blessing that went on for a minute or so, sprinkled it with holy water and then gave it back. (I said the first rosary for him) He was very kind and I felt he gave it a reverence that makes me keep using it, I repair it a lot now, but I love it, so until I break down and get a new one, I still use it.
I have a medal of Mary and Jesus I wear daily I would like to have blessed one day too.