Hello, and I hope i can help you today.
First of all, I want to tell you that the antibiotics you took in the first pack should not interfere with the birth control you took, and the fact that you got a normal period on time means you do not have to worry about pregnancy
Missing two or more pills in a row usually causes some breakthrough bleeding
a few days after the missed pills, even if you make them up. This is the bleeding you are experiencing now. It most likely will stop eventually, but may continue until you finish this pack. You maximize the possibility of stopping the spotting by trying to take your pills at the same time every day. A way you can help remember your daily pill is to take it at the same time as some routine activity you do every day, for example brushing your teeth, or having a morning coffee. Carrying your pills in your purse all the time can also help if you do not consistently stay in the same place every night.
I hope I was able to answer your question today and that this information was helpful.
You should use a backup method of birth control for at least a week after your two missed pills (in case you ovulated then), but after that you can rely on the pill for contraception