Hi Natalie,
Welcome! I'm sorry I don't know a lot about dental care. I do know about injections in other areas of you body - but I am far from an expert in any thing!
From personal and family experience the area where Novocaine is injected can stay sore or tender for several days and sometimes a week. Remember that the area that was injected is associated with the nerves in your mouth - that's bound to hurt.
Do you have any redness or swelling? Are you experiencing any SX (symptoms) other than the tenderness? If not I think it's normal. If other SX appear I'd be more concerned.
However it's never unwise to contact your Provider - in your case your dentist. He/She may have some suggestions like warm salt water - or something similar. Additionally they will certainly know if what you are feeling is with-in-limits of normal. I'd make that call.
Good luck - and please let us know how you are doing.
Take Care,
~Tuck