Pain In My lower thumb and wrist?

I'm assuming it's your fretting hand you are talking about. You could be gripping the neck too tight. The thumb should be on the back of the neck, roughly in line between the middle and ring fingers, not sticking out over the top of the neck. The palm of the hand should not come into contact with the neck. It does not need much pressure to fret a string. The hand should be fairly relaxed. Check You Tube for "Bass, Left Hand Technique".
The wrist of the plucking hand should also be straight. The link below shows good technique for this.




It's also very important to do some gentle stretching and warm up exercises before you play. Again, You Tube has lots of clips on this if you search.

 

Improving your technique will prevent you from working too hard when you play which will increase your comfortable playing duration.

I wouldn't ever try to play through pain (that wasn't fingertip pain) unless I was on a gig.

 

Technique is everything! My suggestion, make sure its right. When it is you can play with a much much lighter touch while still making the same volume because with the right technique you aren't using more muscles than needed.
Try checking up on it with a teacher if you can't handle it yourself! If the pain continues.. time to see a doctor. (A good note to add for that: Ask him if you can bring your bass in to show him what your doing exactly to make it hurt and where it hurts exactly!)

 

You may have a "death grip" on the neck. You can solve that problem by not squeezing the neck between thumb and fingers. Instead the pressure should come from the forearm, ideally you should be able to fret notes with your thumb away from the neck of the bass.

Remember this is pure speculation, if you want to really fix the problem I suggest you take some lessons from a teacher.