iPhone stuck on plug into iTunes screen

I pugged my iPhone in to iTunes on my computer the other day and it worked fine until an unknown error popped up mid update so I pressed cancel and unplugged my iPhone but on my iPhone it just told me to plug my phone into iTunes but every time I plug it in, my phone nor computer read it as plugged in. My phone is now stuck on the screen that tells me to plug it into iTunes. I can turn it on and off and reset it but it is still stuck on the screen. I have checked the plug with other phones and it is fully functional. iTunes is also updated to the newest software on the computer.