2) You lied to cover up your slip.
As the saying goes, more often than not, the slip in and of itself is not as significant as the attempt to cover it up.
Your boss/HR probably saw through your lie (breastfeeding difficulties usually last more than just one day, and you obviously had an "issue" on only one day). If they suspected that you were lying, you would have a much harder time to prevail with your argument, whatever that happened to be.
Take-away lesson: Be professional, conduct yourself unimpeachably, and if you slip, do the right thing - fess up, make amends, and do better next time.