Your pistol is fine. You did not damage your pistol in the slightest. I have a number of 380 cases that were fired in a Kimber 1911 compact in 9mm Lugar. I was at the range and this older man was racking the slide on his Kimber 1911 each and every shot, and being the nosy busybody that I am, chock full of wonderful advice
, I had to see what the problem was. I thought he had not lubricated his pistol, because that has happened before, new pistol, dry pistol, not cycling. After lubing his pistol, and some of his ammunition, we got the thing to cycle once in a while, not reliably though. (lubricating ammunition breaks the friction between case and chamber and facilities extraction) It was not until I looked at the ammo box, and saw "380" auto, did I realize that he was shooting 380 ACP in a 9mm pistol. The cases with 380 ACP stamped on the bottom, would have been an obvious tip off had I examined them. Didn't.
I made the mistake of assuming that the owner knew the proper ammunition to use in his pistol. Closely examining the cases I determined that the smaller diameter 380 brass had swollen out to the chamber walls and formed a gas seal. The brass was good, because it had not cracked or ripped, which can happen in situations where under size brass is fired in a huge chamber.
One of these day's I am going to take pictures of this brass and post them. A couple of glaciers will probably be gone by the time I do this. Florida might be under water too.
The 380 case is shorter than the 9mm, also it is smaller in diameter. At least around the case head. The 1911 has a claw extractor and that held the case head close enough to the breech to allow the firing pin to ignite the primer. Once the powder ignited, the case was shoved against the breech face, swelled up to form a gas seal. The bullet went out the barrel, may have hit what you were aiming at, and because the 380 ACP is of lesser power than the 9mm, your gun did not cycle.
Now if the case head had ruptured, which could happen, not saying it won't happen, and incidentally, it could happen with crappy 9mm cases, then you would have had a whole different outcome. Like what happened when this awful Amerc ammunition was fired in this nice Glock. The case head blew and the pistol sort of disassembled.
Don't worry about damage to your pistol, there should be none, zippo, nada. But don't make this a practice. Might not be so lucky next time.