Medigel and omnigel seems to be kept on one's armour, or carried on one's attire somehow, or stored somewhere somehow. The medigel seems to be applied automatically, somehow, but realistically, it would be applied to the affected area.
As for Dr. Prindle, I was a bit confused that, despite the story set in the 22nd century, he still uses 20th century medical tools. In our most recent case, he happened to have IV and a banana to help Annie's blood level, so she eats the banana while having IV, which heals her of her concussion, presumably.
Annie, here is a useful video explaining medigel, directly taken from the actual game:
https://www.youtube.com/watch?v=Nv4q9gFCnlQ
03-Sep-2017 21:07:04