Mazal tov on the recent birth of your baby!
In general, because of the likelihood of staining during the adjustment period, we recommend starting the minipill after immersing and using a backup method such as spermicide until you are protected by the pill. This is because dealing with staining while tehorah is much less complicated than trying to get through the clean days while staining.
In addition, it is not unusual for postpartum bleeding to stop and start up again. Experiencing a full flow the day after starting the minipill might be a combination of the two factors.
Since you have already started the minipill, there are two possible options for how to proceed.
1) You could stop the pill, let the bleeding subside, and attempt to get through the clean days and immerse. You should then restart the minipill after immersion (using spermicide until you are protected, or abstaining from intercourse until you are protected if you absolutely cannot risk getting pregnant).
2) You could continue with the pill, give yourself some time to adjust to the pill, and attempt to get through the seven clean days once the staining slows down. You can speak to your doctor about doubling up on pills temporarily to help you get through the clean days. There are also halachic leniencies (reducing the number of bedikot, changing white underwear frequently/wearing disposable pantiliners) to help you get through the clean days despite the staining.
There is no clear cut answer how to proceed, we recommend speaking to your doctor.
In either case you should be prepared for the possibility that it may take a few weeks to get this sorted out.
Once you are able to immerse, you should take precautions against becoming niddah from any further staining, such as wearing colored underwear and waiting a few seconds (ideally, fifteen seconds) after urinating before wiping. Some of these precautions are also applicable during the clean days. See our pages on stains and toilet paper for more details.
Taking the minipill at the exact time each day may help reduce staining.
Please feel free to get back to us with any further questions.
BHatzlacha!