I had mastitis once but was prone to plugged milk ducts with both of my babies, especially in those first 6 months.
I work as a firefighter and also teach aerobic classes. So I was very active pretty much right away after the births of both of my babies. I didn't go back to my jobs until closer to 4 months but did start weight training, running and walking and biking etc within the first month.
I now think that it probably was to much and I did feel stressed alot whichi doesn't help.
I'd advice you to continue working out but make sure you get a lot of rest. Nurse right before exercise and directly after to empty the breast. I needed a supportive bra. So if you do wear underwires or a tight bra, take it off right after your workout