If you can reach the wedge shaped piece of paper using tweezers and pull it out, that might work. If not, the only way I have been able to pull out paper is to take apart the entire printer, which is a lot of screws and work.
If you can't seem to take it out after trying the tweezers, then yes, it might be worth getting a new printer.
Please let me know if you need additional help. Thank you.