It could be some form of R.S.I. (Repetitive Strain Injury – a general term which you can google for more info). But no, it doesn’t sound normal and I am afraid you’re just going to make it worse if you carry on playing through pain, because that is likely to only aggravate it. Playing should not hurt, and if it does, you need to stop until it heals. It’s probably being caused by some sort of wear – and the only cure for wear is to stop doing whatever’s causing it. That may mean figuring out a different method of playing.
Not a very positive answer, I know – but RSI can become seriously disabling if it’s ignored and allowed to go on getting worse. (That’s not to say that yours *will* – but I wouldn’t take the chance.)
If your hand position is correct, check your sitting position, and also the height of your stool: make sure the harp is balanced properly and not putting too much weight on you and throwing you out of alignment (asymmetrically-played instruments are notorious for that). See that you’re not sitting too high and having to bend over uncomfortably, etc. You might also investigate Alexander Technique for how to sit and bear loads properly. Sometimes tension in the shoulders or spine can take it out on other parts of you, in surprising ways.
But DO research this, and don’t play if it hurts. That’s your body telling you something and you do need to listen. Really wish I could help more –