So, did the fired case eject ? or is it stuck in the chamber.
are you sure?
How many rounds did you load into the magazine that was inserted just before you took that one shot ( which jammed the gun )
How many rounds are left in the magazine now ?
When the gun went "BANG" do you recall if the slide cycled ?
Did it chamber a new round ?
How many rounds are left in the magazine ?
Are you sure ?
Is there the possibility that there is a live round currently in the chamber?
are you sure ?
You mentioned that the fired case is still in the chamber?
are you sure ?
Okay, only if you are really really sure that there is no live round in the chamber........ here is what I would do.
Remember, there is not much holding the slide onto the frame, so there is not much that can cause the slide to jam.
Remove the magazine
Ensure that the safety is OFF ( i.e. the hammer WILL FALL if the trigger is pulled )
Remove the grips.
Have a look at the trigger bar and make sure that it moves freely.
There is a little tag on the top of the trigger bar that rides up into the slide.
This is to disconnect the trigger bar from the sear when the slide is out of battery.
Make sure that this has not somehow become jammed between the frame and the slide.
If that is Okay.....
Open the trigger guard
insert a 10" wooden dowel into the barrel from the crown end
I would not use a "cleaning" rod as they are usually aluminium, brass or carbon fibre, and do not exhibit much compressonal strength.
Wood is a much better choice and much less likely to damage the barrel.
Dowel will need to be slightly smaller in diameter than .22 ( 5mm would do ) as it has the be able to pass thru the .22 case and push against the inside of the rim of the case.
This will transfer any impact loading thru the case and directly to the face of the breech block / slide.
Make sure that the dowel is all the way to the bottom of the spent case.
Make sure, measure it, and make sure again.
If the dowel pushes on the neck of the case, it could fold it over and make the jam worse, or even damage the chamber.
Maybe also wrap some rag around the end of the barrel to protect it from damage if the dowel breaks and the hammer strikes the end of the barrel.
Hold the pistol firmly and securely, pointing vertical, with the rear of the frame resting on the bench, with the slide hanging just over the edge of the bench. You want the pistol frame to be solid and unable to move, but at the same time, you want the slide to be able to move back ( down ), clear of the bench.
Tap down on the dowel, gently at first, to try and get the slide to move down ( rearwards ) an 1/8" or so. More if it will, until the case is out of the chamber.
This should give enough clearance to be able to remove the barrel.
You may need to manually release the extractor from the rim of the case via a fine pick in thru the extractor slot in the barrel.
Once the barrel is off the slide, you should be able to figure out what is stopping the slide from moving freely.
Take it slowly and carefully. Use a magnifying glass and a good torch so you can really see and understand what is going on.
Good luck !!
ps, if all else fails, take it to a gun smith !