Heya, I am not sure what data set you used, but I found one here https://hub.arcgis.com/datasets/e90996158f0a464189098881379597a6_0
It lists all medium and large airports, including some basic runway information. You get some of runway numbers (not all of them, but enough to get an approximate layout.). And some of the data is outdated. But it would get you closer to the ballpark.
The data set also lists airport codes with the IATA and ICAO codes, so if using the 4 letter ICAO is better than the three letter IATA you can do that.
A few discreps I did find though:
I pulled up KSFO (San Fran) got data showing two runways (01L and 28R), So because we have a L and R, we know we have parallel runways. Obviously not all parallel runways are created equal, (some can be way shorter then the other). So we have runways 01/19 Left and Right, and runways 10/28 Left and right. The headings are also shown, in this case, 28 degrees for 01L and 28 degrees for 208 degrees for 19R. So you can either just use one runway in each direction, or have 2 sets of parallel runways
But like I said, not all the runways are shown, and some are shown twice! I looked up another airport I am familiar with, PADQ (Kodiak AK), which has three runways. However the database shows two? Nope, it shows runway 07 and runway 25...which is the same runway technically (reciprocal headings). Also, you would be insane to try to land on runway 7, there is a mountain right before it. But Runway 25 is the primary runway used for Alaska airlines, so it's the probably why it's listed. Also I said the data was a little dated? Runway 7/25 is actually 8/26 now. They changed the runway number in the last few years back due to magnetic drift.
Hope you can do something with this.
The website that provided the GIS has a even more data sets to check out, like one called "runways" I opened it in google sheets...its huge, it lists 41,586 runways of all sizes, but not all the information is there for all runways because some just don't get used that often. I also open the Airports csv, but it does not list runways, I think the ArcGIS data set is the best bet though, because it combines the Airport data with the Runway data already. But heres the link to the rest of it. https://ourairports.com/data/