Can I Get a Tattoo 3 Days Post- Breast Augmentation?

No Tattoo this early on-you need to wait several months and consult with your PS when it's safe to go ahead with it-you are too swollen initially.

I would recommend waiting until you have completely recovered from the breast augmentation surgery, about 4-6 weeks to be cautious.  There is a risk of infection from the tattoo itself and this can potentially cause unnecessary problems immediately after surgery.