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Inside the crowded train, I felt like I was suffocating.
Literal
Crowded-train's inside [topic-は] breath [subject-が] seemed-to-block-up.
息が詰まる ('breath gets stuck / clogged') is the standard idiomatic way to say 'to suffocate' or 'to feel stifled,' used both physically and psychologically. The ~そうだった ending is the appearance suffix in past tense — 'looked/seemed like it was about to X.' Together: 'it was as if I was about to suffocate.'