The
Boyfriend Shirt look is a trope in romance stories, here she's trying to show off this look to her kouhai (it's not clear if her junior is male or female)... but it backfired on her.
Based on this rather loose translation, her kouhai did not believe she had a boyfriend and thought she swiped one of her dad's shirts to pull off the look. But it's weird to refer to someone else's dad as just "Tou-san" so her kouhai is more likely talking about his own dad rather than hers. And while I'm sure it's more yucky for her to be wearing someone else's dad's shirt than her own dad's, I don't think normal daughters would enjoy wearing their own dad's shirt as well, so her reaction does not line up if the scenario was her using her dad's shirt to pretend to have a boyfriend.
Alternatively, her kouhai IS her boyfriend and she tried to flirt with him saying:
"Check it out, I'm wearing my boyfriend's (your) shirt!" (<- this is basically what the title 「彼シャツだぞ、後輩ぃ」 means)
And then he says それ父さんの…かも "Um, no that looks like my dad's... I think." causing the mortified look on her face.