I know exactly how you feel.. I had pneumonia when I was pregnant, and was on amoxicillin, which did nothing ... I had to start on IV Keflex the day after my daughter was born. So I was able to nurse her for only that day, so she got the colostrum but I couldn't continue. "Pumping and dumping" was not only heartbreaking, but exhausting as well. I was ill, and having to wake up every 2-4 hours to give her a bottle, and then pump my milk and wash it down the drain was awful. I cried and cried.
Because of my fatigue, I chose to continue bottle feeding. I just had to sleep,, I had no energy and a 4 y/o to go home to. I felt terribly guilty because I nursed my older daughter for eleven months, and it was a wonderful experience...and I wanted that with my little one too. I ended up being on antibiotics on and off for four months while the pneumonia resolved. So in retrospect it was the right choice for me.
Now my daughters are 17 and 13, and there is no difference in their health ( well, my older daughter actually has had more colds and ear infections than my younger daughter) and my bond with my little one is just as strong as it could ever had been, nursing or not.
Don't beat up on yourself. Do what you can to take care of both yo and your children. No matter what you choose to do know that it will all turn out fine.