A couple of hints as to what is causing this.
1. The removal of paper, if it was rough, or if the paper was badly caught in the works, may well have put some cams out of order, or out of position.
There could be other things wrong also. Was the paper caught inside the printer, under the ink cartridge carriage perhaps?
Pull the power plug on the printer.
Open the printer, examine the interior. Grasp the carriage, if it is in a position to be grasped. See whether gentle pressure on it can move it back and forth - do not force it to move nor exert much pressure.
Note whether any loose parts might be caught in the works, or whether the carriage is at an extreme position to left or to right.
Note whether any parts are just plain flopping around loose in the interior - perhaps a thin plastic strip might have broken and be loose?
2. A screeching noise often indicates a misaligned or damaged paper feed roller. Open the printer cover and inspect rollers for debris or wear. Clean rollers gently with a lint-free cloth and isopropyl alcohol. Check for any torn paper pieces stuck inside the feed path. If rollers are worn, consider replacing them. Regularly clearing paper jams carefully and avoiding overloading the tray helps prevent this issue.
