It looks a little bit like voile or lawn.

This fabric is heavier/thicker. More like a linen but looser weave. You can't see through it. Doesn't drape.

Around here, we don't have fabric stores with knowledgeable folks, so there's no one to show the fabric to ask.

Thanks for trying.

According to the web, Cotton Comfort is now put out by a company called Eczema Clothing. You might check with them: https://eczemaclothing.com/collections/cotton-comfort

Otherwise, my first thought upon looking at your photos, was "seersucker". I know Hobby Lobby sells seersucker, or at least they do here at my HL (Midwest).

I know this fabric, have had clothing made from it, but I don't know what it's called. After Googling "types of cotton" and checking websites, I still don't know. I hope someone can find a name for it.

Not even in the ballpark of seersucker. Seersucker has a distinct repeating pattern of small puffy sections.

Looks like unbrushed cotton flannel to me.

Picture of double gauze for comparison.

I remember fabric like that from back 'inna day. It had a sort of a springy feel to it, but, like you said, no stretch .

No worry about it, though. Even if you knew what to call it, it is very, very unlikely that you are ever going to find it. Those old fabrics are not even being made anymore. Lots of fabrics that used to be common are no longer to be found.

I have a remaing piece of what I think may be the fabric that you talking about. I made my little girl a robe from it and she is now middle aged. But I still have this remnant of it. I think it may even be the same color as in your photo.

Since it was a big enough remnant , I put a hem on it and use it as a small blanket.

It does have a kind of a gauze kind of vibe to it.