Breastmilk has probiotics. I don't think eating probiotics would increase the probiotics in breastmilk. A year of antibiotics! That must be a very serious infection. Has your baby been tested for primary immune deficiencies (PID). My 3 children and I (adult onset for me) all have a PID called common variable immune deficiecy (CVID). We were all diagnosed right after the birth of my youngest child in 1988.
There are 10 warning signs for primary immune deficiencies. If a person has 2 then they should have testing. Your baby has at least 1. The good news is if your baby has hypogammaglobulinemia, low levels of IgG, it can be treated. She can get IVs of IgG every 3 weeks to help her fight infections and protect her from getting infections. They would probably implant an IV port under her skin and getting the IVs would involve minimal pain. I've been getting the IVs since 1988.
Here is a link to the 10 Warning Signs for PIDs