I get this too. I've been touch typing for nearly two years, so I doubt it goes away as (or even if) the muscles get stronger. If it hurts, I'm guessing I'm just developing carpal tunnel or RSI. There's a few things you can do to get rid of it:

1) Make your keyboard at the right height. I don't really know what this height is. If you hold your elbows to your sides and your arms in front of you, so your elbows make a right angle, I think it's just above that.

My posture is shite, I like to sit cross-legged on the chair with my elbows on my legs, and rest my wrists on the desk in front of the keyboard, but this makes typing very comfortable. Alternatively sitting up straight works.

2) If your keyboard has rubber feet, don't use them. Put your keyboard as flat to the desk as you can. If it tips towards you, you tense your forearms slightly by bending your wrists upwards.

3) Don't put the keyboard in the center. Put it so that your hands are in the center. The area between the two Ctrl-Keys should be in the center, and everything to the right is just a massive tumour hanging off the side of your keyboard. I wish the numpad (or the arrow/home/pgup area) was on the left. That would make more sense.

4) The less you use the mouse, the better. The mouse makes my forearm hurt when I use it too much. Whatever programs you use, learn the keyboard shortcuts. I take this to the extreme with i3-wm, vim, and qutebrowser (or vimperator), so I can easily go all day without touching the mouse once. You probably won't want to go this far but I can't recommend vim enough. If you can touch type, practice vim, and you'll never go back after a week or two.

5) Consider DVORAK (or one of the others.) Since I learned the layout, the pain has been much less. Other people say DVORAK eases pain but it's still possible that I just happened to find the perfect keyboard height at exactly the same time as learning DVORAK. My forearms don't hurt any more, and it's definitely not placebo, but whether it was DVORAK or not I can't tell. But it probably was.

6) When your arm hurts, massage the shit out of it. I just squeeze it (with my thumb on the painful top muscle) over and over up and down the arm. Makes the pain slightly better temporarily but I don't think it really fixes the problem. I also stretch it by twisting my (right) arm upside-down counter-clockwise and then bending my wrist in (fingers towards the ceiling.)

7) Take breaks. (Obvious.)