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Taka I didn't think I would have a cold, but the other day I caught one.

Yes, it's fine.

Good. Thanks, Avangi.

By the way, if comma were added after 'the other day' as:

I didn't think I would have a cold, but the other day, I caught one.

would it be OK?

I think it's better without, but the comma would not be incorrect if you wish a pause there.

I meant to edit and comment on the time factor in your original, but I wasn't quick enough.

I didn't think I would have a cold, but the other day I caught one.

With both clauses in the simple past, and no adverbs of

In terms of the time factor, what about this?

I hardly had any cold last year. So I didn't think I would have a cold, but the other day I caught one.

I think the passage, or the flow, of time is clear here. Don't you think so?

yes.

Good! Thanks, Avangi!