I'm nursing, but have bad anxiety, depression and mood swings. What's a safe medication to take? That won't harm baby.

Talk to your doctor. One that is often used is sertraline since it is regarded as safe with pregnancy or breast feeding. The brand name is zoloft. You should see your doctor if you are having symptoms of depression. It is actually very common after delivery. Overall med are only part of a solution.
Mood swings do. Have a hormonal component after pregnancy. Medication is an answer for some. I have had positive experience as well with chinese medicine and homeopathy , both of which are safe for mom and baby. Acupuncture is excellent at balancing hormones as well. Craniosacral therapy also has great benefit in treating post partum blues. Good luck!
Talk with your doc. Most anti-depressants are passed into the breastmilk, but in very small amounts that probably will not affect your baby. Talk with your doctor to see if starting one is right for you. Studies show that maternal (and paternal) depression can negatively affect a baby's development.
Nursing. As a general rule, it is not advised to nurse while on medications, since the medicine can be transmitted thru milk and exert side effects on baby. Consult the pediatritian for bottle feeding and advise.
None. It hasn't really been proven breast milk from moms is safe as it is difficult to perform such a study. The safest thing is to not nurse while taking antidepressants. Your child may benefit by you taking antidepressants due to the improvement of the attachment and binding process which could become compromised if you are too depressed. Then you would have more troubles and feel worse. Talk w/dr.