Let me help you decide if it could be Carpal Tunnel.
The Median Nerve is involved. It serves the thumb, the first finger, the second finger, and the inner half of the third finger. It does not involve the half of the third finger closest to the "pinky", nor does it serve the "pinky". So if your "pinky" is involved in the 'finger throbbing', it isn't likely Carpal Tunnel.
What to do? The way you hold the phone obviously needs to be changed, and I suggest using a earphone with a microphone, so that you don't have to hold the phone.
Also, I suggest Vitamin B-Complex, it's the B-6 that can be helpful for Carpal Tunnel. Also, for a steady muscle cramping, I suggest a dishpan with warm water and a fourth cup of Epsom Salts to soak your arm in, since the muscles for your hand are in your forearm.