If you are experiencing having your iPhone screen stuck at iTunes, it is likely that your iPhone OS has been corrupted or just went out. Below are the methods you can do to fixed it.
Pressing Volume down key together with the side button will do a force boot on your iPhone. If it does not work proceed with method two.
Download and Install ReiBoot then connect your iPhone to your computer. Make sure you are using the correct application for your Operating System. If you re using MAC, download the mac version and if you are using Windows, download the Window version. Once you install the software, click the Update. This will update your iPhone OS. If it does not work proceed with method three.
Since you already did a force restart and OS update and still doesn’t work, the third method would be to do a factory reset. Using ReiBoot again, select Reset/Fix All and this would take a while. Note that doing a factory reset would erase all your data so it would be best that you have a backup before doing this or fine with deleting your iPhone data. If you are using iCloud service, then you should be fine.