Were you playing the Fender sitting down or standing?
If it was hanging off a strap, a couple of factors could be involved. Here are two that immediately come to mind:
1. How heavy is the Fender compared to your Dingwall?
2. How high or low does it hang on the strap?
3. Does it neck-dive, if you take your hands off the bass?
Weight may matter, more than you would think. For instance, I'm having a pig of a time right now with bursitis in my left shoulder. I can play any of my basses seated, but I can't go more than about 20 minutes if the weight of the bass is hanging off a strap. Even the Dingwall, which is my lightest...
Strap height affects a bunch of stuff related to hand mechanics. Try raising or lowering the Fender, to see if it helps.
Neck dive puts extra stress on your forearm, wrist and hand muscles. For a healthy person, it barely matters. For anyone with CT or other RSI's, it can be enough to send them off the deep end.
Anyway, if you were playing sitting down when all this started, then it could be the neck profile on the Fender, and/or the (slightly) more contorted shape that you fretting hand has to take on a parallel-fret bass.
Some people with CT find that narrow necks (i.e.; your typical Fender Jazz) aggravate their wrists and hands as much or more than a big, wide 6 string. This is a very personal thing.
My dad had to have a couple of hand surgeries towards the end of his career. Not just CT, but osteo-arthritis as well. Regardless, he got hooked up with a hand specialist in Toronto who had specific experience with musicians.
If you're already talking to someone, quiz them a bit. They might be able to look at your posture when you are holding your basses in playing position, and make suggestions. Even better, they might make a referral to someone who has worked with musicians before...
In the meantime, if the Fender is hurting you, leave it on the shelf for now.
In the long run, CT can be a problem that gets worked out with some help, or it can end up being a career-ender. This is not something to mess around with!