Do bicep/tricep workouts work out your forearms too?

I do individual workouts for my biceps and triceps and I can always see my forearm flexing with veins and muscle popping out (Im skinny so its easy to see, just started working out), so I assume it works it out too because lets say when I do bicep curls and I max out and I put down the weight, I can feel the burn in my forearm too but not as intense as my bicep but almost there. I would work out my forearms too but I dont want them to be as big as my upper arm though, you know? It would just look weird. If I just dont do any forearm weight lifting at all will they stay the same size or gradually grow as my upper arm grows?