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西松屋で大泣きしている生後2ヶ月くらいの赤ちゃんがいて…
→ “There's a baby about 2 months old having a huge meltdown at Nishimatsuya...”
西松屋 nishimatsuya = Nishimatsuya (noun, proper noun: a Japanese department store chain)
で de = at / in (location particle)
大泣き daonaki = crying loudly / sobbing (v.)
大 dai = big / large
泣き naki = cry / weeping
している shite iru = is doing / is currently in the state of (v. progressive form)
し shi = do / make
て te = connective / continuous marker
いる iru = to be present / to exist (auxiliary verb)
生後 kogō¹ = after birth (time expression)
生 sei = life / born
後 go = after / behind
2ヶ月 nikagetsu = two months (number + time unit)
2 ni = two
ヶ月 kagetsu = month(s)
くらい kurai = about / around (approximation marker)
の no = of / possessive particle
赤ちゃん akachan = baby (colloquial/noun)
が ga = subject marker particle
いて ite = there is / staying (te-form of 'iru')
… = ellipsis (indicates trailing off or implication)