Think backwards. (Or as my professor put it, "Back thinkwards.")
It's very uncommon for anyone to "draw first on a computer program and reverse it;" that's an unnecessary extra step and one that, perhaps obviously, did not exist at the birth of printmaking, which has existed far longer than digital technology.
While I typically wouldn't refer to any tool as a "crutch," in this case, I think it does apply--not to you specifically, but to each person I've worked with who fixates on the idea of "I need to draw it the right way and reverse it." By leaning hard on the idea of needing those extra processes, you're stopping yourself from learning how to think in reverse. Learning to letter in reverse isn't all that hard; the worst part of it I've ever encountered is second-guessing if I have the letter the right way because I've gotten too accustomed to reading in both directions (this can be double-checked by writing the letter or phrase in the correct direction, or having another person look it over).
Let go of the "crutch" of technology. Will you make mistakes? Yes, probably. So what? Mistakes are just learning opportunities, and if you stay where it's "safe" you never learn. Work fearlessly, without fretting about mistakes or twisting yourself up about them.
In the case of something particularly difficult, such as a foreign character set or a design that must face a particular direction, it's okay to lean on technology a bit. But it's still not particularly necessary, given the myriad other ways that can be used to reverse a simple graphic (such as a linguistic character). You can use a light box (or a window if a light box is not available) to trace to the backside of a piece of paper. You can use graphite transfer processes to copy it over to the linoleum block. And yes, you can use a mirror to double-check yourself. But the most useful process is to learn to think backwards and let yourself make mistakes.