You can do it...because you DID do it! Ditto, ditto, ditto giving yourself a rest day between ride days until you build up more stamina. You will feel when you're ready for regular riding most days. Three-Speed? Generations of Brits made do with just three-speeds (or less) on bikes weighing much more than yours. As far as ride time and average speed...those are not your challenges right now, if ever. The challenge right now is to achieve the level of fitness that allows you to enjoy your commute; and the best way to do that is to ride your bike to work! FWIW: I've been bike commuting seriously for almost 25 years, and have had a few major interruptions to my routine with one totaling over a year. The first few rides after a lengthy interruption of even a month, provide all the agony, pain and effort of when I first started. And those strenuous initial commutes can take 33% longer than later when I am "up to speed". If you had the gumption and drive to attempt bike commuting, you have everything you need to stick with it.
go, Go, GO!