Let's start by looking at those hospital locations. You have address information, but to find out where those addresses are, you need to "geocode" them to get Latitude/Longitude values. This can be done for free by Googling each address, or by using a paid service like the spatial "Location Insights Dataset" available from Alteryx or using an API available from various third-party vendors.
Now that you have Latitude/Longitude values, you can use the Create Points tool to create spatial objects in Alteryx. A Trade Area tool can then draw the requested 10, 20, and 30-mile rings around each point.
Now that those trade areas are prepared, prepare the patient records by geocoding them and using the Create Points tool to assign a point spatial object to each record. In the attached example, I randomly generated patient records to show the rest of the matching process.
Once you have prepared spatial objects for the trade areas and patients, use a Spatial Match tool and then Summarize the results.
