Yeah, changing the freewheel is an easier and cheaper alternative.

You're on about 75 gear inches right now, which actually nets you 20mph at a cadence of 90RPM. This is not slow.
Why do you feel the need to gear up?

If I were to recommend changing the freewheel at all, it would be a 16t freewheel. About 80 gear inches. 21mph @ 90RPM.