Most bowling balls have similar specifications for weights between 16 and 14 lbs. When you get below that, most bowling ball companies offer a generic weight block plus filler for lower weight balls.
Also, I don't think there are many companies that advertise what the core looks like for various weight balls for a given model of ball; however, Storm Bowling does show what the weight block looks like for their balls.
In general, they'll show one type of weight block for 16 - 14 lbs.; however, for their highest level of balls, they do have the same type of weight block inside of the ball.
The difference between one 12 lb. ball or lighter and another is essentially the coverstock and not the weight block spec's, except for the highest level balls that they provide.
Talk with your local Pro Shop
owner/operator and they'll help get you on the right track.
Take a week or two off from bowling and rest that arm. Once you feel like you're able to get back to the lanes, I suggest that you find yourself a coach to watch you bowl. You're likely using way too much effort to bowl. You're arm should be the pendulum for the ball rather than forcing anything. Use gravity more and you'll enjoy swinging that ball much more... Hope this helps...