Pretty much what was previously mentioned.

There might be a label on your rim that tells you the ISO formerly ETRTO size of the rim. It should look like the very small print on this rim


The 622 x 20. Sometimes you see it written the other way 20 x 622. Maybe that's when the tire and rim mfr aren't quite going by ISO standards.

Anyhow, the 20 is the internal width of the rim in millimeters. Once you know that you can look at the recommended tire widths for what you might want to put on them. They sometimes vary from manufacturer to manufacturer and some might consider them conservative and go outside that recommendation.

Here is a chart from Continental Bike Tire with their idea of proper rim to tire sizing.



As for getting more speed out of your tire, play around with the tire pressures. A little higher or lower might help. Some only believe what a chart or online calculator tell them. But I'll ride the same pressure for 12 rides, then change to a different pressure and do another 12 rides and based on what my data shows and my legs feel, I'll zero in on the ideal pressure for me on the road surface conditions I encounter.

However if you ride for longer than 60 minutes and you are going up a lot of hills or a lot of stop and go, then you might just be wearing yourself out with a frame that might weigh almost twice what a decent road bike might weigh.