Dear TamJam: Thanks for waiting for a reply. No, I would urge you to continue taking your BCP as prescribed unless your GYN says to stop. Even if you stop the BCP you may continue to have a hormone withdrawal bleed for a while--plus be unprotected from pregnancy after a week.
Yes, if you have persisting breakthrough bleeding problems on your current BCP, a change in brand or formulation may be helpful. Your GYN can help you sort out which other BCP might offer better cycle control.
Alas, breakthrough bleeding is very common in most all hormonal forms of birth control. The worst times tend to be either in the initial few months as the lining of the uterus is "getting used to" the hormones, and then again after years of use when the lining of the uterus can become very thinned out (making it less stable).
Hope this is just a transient problem due to being a new start on your pill.
Yours,
Jane