If you filter using a table calc, all the data remains in the underlying table, but the sheet displays only those rows that fit the table calc filter criteria.
I recommend that you upload a sample workbook so that someone can work with you in a concrete example. Trying to explain it conceptually will almost assuredly result in a frustrating thread.
You're talking about hospital and doctor data, so I'm sure you will have concerns about proprietary issues. So check out the demo video to attach anonymized data. Video can be found here: