D.W.
I'm not sure it's your baby necessarily. It's possible that she's adding dirt and bacteria to your skin, but acne is usually dirt, oil and bacteria being trapped by a clogged gland and causing an infection.
I'd first try over the counter products with benzoil peroxide 10% as they're generally safer. Salicylic acid products are not recommended during pregnancy, but you may want to ask the pharmacist for nursing regarding absorption into the skin.
It may also be coincidental that the acne is on your chin. Because you're nursing, you still have several abnormal hormones raging through your body, and it could be completely unrelated.
A good cleanser and some topical antibiotics (as mentioned above) will help most people. Unfortunately, I have adult cystic acne that is only manageable with Rx products and is exacerbated during pregnancy/postpartum.
Good luck!