Does this mean missing a dose or two would be painful?
I depends on the medication and how you personally react but I wouldn't say it's very physically painful to miss a dose, though long term going on and off over and over is bound to mess up something. SSRIs have a lot less side effects then SNRIs so keep that in mind when you're asking the doc about it- though if it's your first time on antidepressants they'll probably just chuck a low dose of prozac at you which is an SSRI so isn't as crazy with side effects.
The closest I've ever gotten to physical pain from antidepressant withdrawal is brain zaps where missing a dose makes you get this weird zappy bit of pain in your brain that's on and off throughout the day. I'm not sure how to explain that properly maybe someone can do a better job for me TT
Emotional pain would probably happen though, skipping doses can make you go downhill emotionally very fast if you're not careful. When you start taking your meds there's a good chance you'll feel worse before you get better as well. There's a risk of becoming more suicidal, especially if you're a young adult. This isn't because the meds wanna make you kill yourself more- it's more like you now have the energy to follow through on that impulse and are more emotionally vulnerable so can get triggered more easily.
Just make sure to surround yourself with people as much as possible, they will notice the changes in your behaviour before you do and keep a journal like the over folks have already said.