Re: Weird Left Hand Discomfort - Help!
I tried holding my mandolin like you are, and it would hurt my finger in the same place if I were to do it any time at all. I would agree to work on changing the position of your hand. As soon as I went back to my usual position I noticed my finger (where yours is sore) did not even touch the neck.
Re: Weird Left Hand Discomfort - Help!
There are basically two approaches to playing necked stringed instruments. You can play this way (such as the OP pictured): you can play using only, say, two or three fingers on the fingerboard. But if you want to use your pinky - which enables vastly more dexterity on the fingerboard - you'll need to change to the other approach.
A more ergonomic, economic approach is to turn your hand so that the palm is basically parallel to the neck, or "facing" the neck - which enables better access for the fingers. Maintaining your wrist in this position, knuckles are basically aligned along the neck/strings plane. This allows your fingers to be in a "ready" position at all times (basic ergonomics/economics), rather than having to turn your wrist when you want to get your pinky on the fingerboard. I think Pete mentioned this - keeping your wrist in proper position allows your fingers to be ready and able at all times, instead of having to turn your wrist...watching folks' hands flying around is disconcerting for me.
The thumb can be either up or laying back along the neck. Tons of players have their thumb up - I can do either, but mine tends to be up, a remnant of string playing other instruments - on cello the thumb is opposite the second finger; on hardanger fiddle there's not much room along the neck, etc. So, the thumb goes wherever is comfortable.. (There's also the aspect of "collapsed" wrist, often seen in folk fiddling, and straight wrist such as in classical violin position). Here's Paddy Glackin
https://youtu.be/jbkgV6Fx2yI
Notice here the economy of the fingers.
https://youtu.be/Fb2A5H6gUMY
There are styles of playing that require prolific use of the pinky finger. If you want to range and play other styles, other instruments, you might consider adopting this approach.