So there wasn't an expiration date on the yogurt bottle?!

Most yogurt has a "Use By Date" on it which is not exactly the same as an expiration date. I have eaten some yogurt after its "Use By Date" but that's only about one or two weeks later at the latest. You can also totally eat yogurt past its expiration date--but probably only at one or two weeks tops. In OP's case, there could have been other signs besides a bad smell that her yogurt went bad such as discoloration or excess liquid.

Even without a sense of smell and an impaired sense of taste; you should have known something was off

At least you won’t be able to smell what’s about to come exploding out.

I've never had a cold so bad that I wouldn't recognize bad dairy.

You’re actually supposed to stay away from dairy with a cold, it can lead to making it worse. That sucks though, OP.

All foods have expiration dates on them. You should have checked that. In fact, you should always check that - never rely only on your sense of smell.