Why would my two year old dog be having a milky discharge coming from her nipples?

She's intact? That is usually going to happen to intact females. Pregnancy, false pregnancy, season, and hormones (possibly an imbalance) are some of the more common reasons, may possibly also be there are other signs that you might look into something like her thyroid. Give your vet a call and speak to them about it to make sure it's nothing to worry about or if maybe you should just get her checked out after they are able to get the details.
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