I was on Micronor (mini pill) when I was breastfeeding. I know that you have to be quite accurate with those pills, about when you take them (exact same time each day) because they are not nearly as effective as the combination pills, seeing as they contain progesterone only and no estrogen.
I've switched to a combination pill and, although you should be aiming to take these at roughly the same time each day, it's not as important that you do so. I mean, if you're off by a half our or even an hour, I don't think it's going to affect the effectiveness. Prior to conceiving my first son, I was on the pill (Marvelon) for about 5 years and I didn't take it at the exact same time each day - and I never had any problems.
With any pill, it's important to establish a good routine - having an alarm on your phone is a great idea! - but combination pills really are so much more effective than the mini pill. Of course...as your doctor mentioned, there are other forms of birth control out there that might give you more peace of mind...or you could always use a back up form of BC (ie. condoms and spermicidal lubricant) while on the BCP.
Good luck - I hope you find something that works for you :)
Ok well my doctor answered my question. She said that if I was nervous about missing then I should use the patch or the ring.