Without being to physically see your thumb, and the fit of your ball, it is impossible to say positively. But I would be willing to say that you need to seek a competent fitter/driller.
Have them check the span, thumb pitches, and size of the thumbhole. It almost sounds like you may be squeezing the ball (bending the thumb) thus causing the soreness/cuts.
Best off to find out who drills/fits for the top bowlers in your area, and have them check it out.
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