She'll get better if she just gets some antibiotics and sleeps it off.
Literal
She [topic-は] antibiotics receive [and-て] sleep-[conditional-てりゃ] heal [probably-だろ].
抗生物質 'antibiotics' — a medical term. 寝てりゃ is a casual contraction of 寝ていれば 'if she keeps sleeping' — the conditional of the progressive. 治るだろ is a blunt male-speech prediction: 'she'll probably get better.' The tone is dismissive, treating the illness as minor.