Shower smells like mildew. Please HELP!

We moved into a house a year and a half ago. Never had any problem with bad smells in the shower until now. The house was built in the 1960s.

The shower walls are tile. I didn't clean the shower for about 9 months after we moved in, and we never had a smell, which is why I don't understand why one just now appeared, when I clean the shower regularly. The smell can't just be from mildewed tile or grout due to regular shower use.

I've ruled out the drain. Drano didn't solve the issue, nor did bleach, and when I put my nose by the drain, it really doesn't seem to be coming from there.

A few weeks ago, the smell would occur right after turning the water on, but now, about a week later, I can smell it immediately when I enter the bathroom. I've tried pinpointing the smell by sniffing around in the shower, and it really just seems to be coming from the tiles.

I don't guess there's a possibility that there could be mold behind the tiles, since we've never had a problem before, and the smell appeared suddenly out of nowhere one day. We did have some grout that was chipping away, but my husband re-did that last week. He used to do tile for side jobs and he swears there is no way water could have gotten behind the tiles, because of the way the grout was chipping and how thick the tiles were. I assume he knows from experience, but I'm just not convinced.

I'm really hoping someone can help me out. This is driving me crazy, and I can hardly stand to use the shower the smell is so strong. I don't know what to do if I can't get to the root of the issue. I can't afford to tear out the shower to see if there is a problem behind the tiles. Why would the smell just appear from nowhere after so many years?