I was backflushing my machine and now the portafilter is stuck

you have a leaking pressure relief valve. You need to replace it.

If the shower holder is stuck, it it probably stuck with lime or coffee oils. You could try backflushing with a little descaler if the gasket is still in place. That will dislodge some of the lime and then can be pried off with a flat screw driver. In case you damage/ break it - you can get one here. Gaggia classic portafilter

You need to check if you have the solenoid valve, if you do, then back flush regularly to avoid group blockages.
You would want to descale regularly as well to avoid the solenoid blocking.
JURA descaling tablets

Hi
Your 3 way valve is dirty or bad. Have you ever done a back flush with a detergent?
About every 3 months it is a good idea to do a backflush your machine with a blind filter basket. When backflusing you should only use a good espresso machine cleaner designed for an espresso machine's brew system. DO NOT USE a decalcification cleaner. First, clean the screen and dispersion plate plus the brew head and reassemble, which will prepare you for backflusing. Then, insert the blind filter basket into the portafilter with a ½ teaspoon of cleaner in the basket. Next, place the portafilter into the brew head and tighten. When the machine is hot turn on the brew button for about 10 seconds and then turn off. Then, wait 30 seconds to a minute. Next, turn the brew button on again this time for only about 3 to 5 seconds and then turn off. Wait 30 seconds to a minute. Repeat these last two steps six to eight times. After you have completed the backflushing remove your portafilter and rinse the blind basket with fresh water. Next, you turn on the brew switch to rinse the plumbing. Then, reinsert the portafilter into brew head and turn on the brew button for about 10 seconds and then turn off. Next, turn on the brew button for approximately 3 to 5 seconds and then turn off. Repeat about 4 to 5 times. Always remember backflushing is hard on electric 3 way solenoid valves, so it is not recommended do this no more than four times a year for a machine used in home application. You will find more good is done to your machine be properly cleaning the brew head.

The blind filter is used to backflush the group with espresso machine soap to get rid of the coffee oils.

You have a stuck check valve. Try running the pump with the steam knob open, then shutting it then, opening it 4 or 5 times and see if it will pop open. Make sure that you don't have the portafilter in at the time you are doing this.

It is possible that a regular rubber disc from a commercial machine might fit, check with the nearest espresso machine dealer.

There is apossible restriction, but, whatever actuates the rrelease valve is what is actually malfuctioning.Depending on you level of detertermination, you can follow my approach to the dilemna if mass production. Since it doesn't work, find out why! Worse case scenario is the trash can, the best, A better understanding and working knowledge of the appliance. Screws usually hold these things together. Expresso machines are not inexpensive and there is a reason for those big bucks. No glue! So always taking the electrical part into consideration, there is no reason you cannot disassemble the unit and entertain yourself while at the same time learn something. Always take the approach that someone assembled it and you can disassemble it. If it does have glue, rhen it was anever intended to be serviced or repaired by anyone. So give it a shot and if you run into a problem, Give me a holler and we will keep moving. My ph. # is 909-630-3192. You may have to send me a picture or two of our project, So have a camera ready.... Ned

The group head gasket needs to be cleaned or replaced. First get a brush and clean put the head, then insert back wash filter(basket with no holes) in portafilter, make sure that it is seated properly(atleast 90° angle with machine), then run the head if nothing leaks around the portafilter the gasket is fine, if it leaks then replace the gasket. Make sure that you press the stop button before removing the back wash filter.