Outer wrist/palm pain, what is this?

because you said it goes partially into your outer palm i think it could be a injury with your pinky. Has there been any swelling? It could be carpal tunnel but i cant really say you should probably go to a doctor and get it checked out for sure and they could tell you what to do you could probably get to a physical therapist or if it is carpal tunnel if it worsens you could end up having to get surgery so i would go to a doctor and have them tell you exactly what is wrong and tell you how to cure it. Better safe then sorry.