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It would help to know more about the revolver. Predating the .38 Special was the puny .38 S&W Long. Predating that was the even punier .38 S&W.

Firing .38 Special in either of these risks severe injury and destruction of the revolver.

The .38 Long Colt is close enough to .38 Special that you might get away with it, but it certainly isn't recommended.

I'm thinking that most revolvers chambered for .38 S&W Long would have cylinders too short for .38 Special, but that can't be counted on. If the cylinder is long enough, it is probably bored through so that the Special round might fit, but with possibly disastrous effect.

Definitely, do not fire any more Specials. If the gun is sound, you might still be able to use it with the correct cartridges. Try to identify the gun. It might then be possible to learn in what calibers it was offered. I can still purchase .32 S&W, .32 S&W Long, .38 S&W, and .38 S&W Long for my revolvers. It may be that .38 Long Colt is also available, if that turns out to be the correct caliber.