Problem with my usb plug
Without the center part of the USB plug, it should be possible to make some deformations of that shield without damaging rest of the usb connector and pull it out. Aim for the weakest spot - seam (usually in the middle of bottom).
But even if you damage on board connector, it can be replaced (but it might be better to give it to someone with soldering experience - at least for unsoldering it)
And as noted in comments, even without working usb connector it can be programmed either by connecting USB-TTL serial converter to D0/D1 (but without auto-reset, unless you provide 100nF capacitor between reset and RTS), or it can be programmed by another Arduino as SPI (it needs bit more wires, and by default it doesn't burn bootloader, so if you fix USB, you'll have to burn bootloader).
Easier might be swapping Atmega328p between boards, however it needs some practice, so you won't bend or rip pins)