Have I burned my Arduino Uno?

Hello all. I have connected my Uno to the power socket with a 12V 0.3A adapter, to the 2.1mm port.
I have already did connected it that way before.
The 7segments that are connected did not work like expected (it did work just prior to that) and the Uno and the sensors were very hot to the touch.
I noticed that this time unfortunately I have accidentally connected 2 Hall effect sensor switches to the Vin instead of the GND.
Since then it becomes very hot even when I connect it to the pc using the USB port and I can't download my programs to it, although the ON led is on and my pc recognizes the UNO. As said, It also doesn't work properly.
Could my connection mistake cause this?
thanks

did you create a short circuit?

It does sound like the Uno was permanently damaged, although the damage may be confined to the on board voltage regulator. That could be fixed, but only if you have the right equipment.

Buy a new one and chalk it up to experience. We've all done something like that, more than once. I try to remember to triple check all connections before powering up a new circuit.

Thank you for your reply.
Could the connecting mistake (Vin instead of GND) cause the permanent damage? Electricity wise

Yes, you connected 12V to the 5V feed, this WILL damage the chip.

No I have connected the 12V to the 2.1mm port. I have connected the 5V from the arduino back to the Vin.

VIN is connected to the 12V 2.1mm port. I do know what I'm talking about!

I just thought I might have not explained it correctly! I'm sorry.
So guess I did burn it...damn