Yes, if your using desktop monitor is 2 or 3 feet away, that's an intermediate distance and neither reading glasses nor driving glasses will provide the optimal sharpness. If your "computer work" is a laptop monitor, a prescription for reading glasses (~12 inches) may also work for that shorter distance.
>Do you just go to the optician with the glasses?
No, I order them online: https://www.google.com/search?q=glasses+online
Those websites let you type in the numerical values for sphere, cylinder, etc. You don't need a prescription. (It's the online contact lens websites that require a faxed prescription or a confirmation phone call with the optometrist.)
If you need a tutorial for how to use a trial lens set, there are lots of youtube videos and text websites explaining SPHERE, CYLINDER, AXIS, ADD, PD, etc. It's really easy.
I used www.zennioptical.com but the others websites have good reviews as well.
If you absolutely must use a local optician such as LensCrafters, EyeMasters, Pearle Vision, Costco, Walmart, etc because you need to try out the frames on your face, a trial lens set isn't going to be as helpful to you.
Anyway I wanted to ask about your test lens set. Do you just go to the optician with the glasses? I get the impression they’d give a reaction as if you are self diagnosing from something you’ve read online...