You could maintain authenticity by storing hashes of data in the blockchain. However, storing the data itself ( even when its encrypted ) in the database might not be the best idea.
I’m not a medical data storage expert; when I think of medical data I think of MRI and CT imaging, scanned consent forms along with some arbitrarily key/values pairs. Before making any concrete design decision, I’d suggest you’ll figure out what is the min/max/avg data size. If that data size exceeds several kilobytes per account, then it might not be the best fit for a blockchain ( any blockchain, not Algorand specifically ).