ESH

clearly labeled on the door "Mothers Only"

Here's the thing. The room is available for women to breastfeed in private, not so much for them, but for the public. Because the main complainers for women who breastfeed in public are those who accuse women of doing a "sexual act" out in the open, and mothers usually fight back by accusing the public for sexualizing a completely natural act of feeding. For some reason or another, you're going to opposite route, calling a 13 year old boy a "man" and being uncomfortable in his presence, even though he has a 2-3 year old sibling and he's probably seen his mother breastfeed hundreds of times and it's seen as a completely normal non-sexual act for him, exactly the message pro-breastfeeders are trying to tell. You certainly were "sexualizing breastfeeding" and was probably making the 13 year old boy uncomfortable.

She didn't need to call you a bitch though. Really, the correct thing to do was tell the nurse, which you did, but you should have done that first.