Could an eyebrow injury cause nerve damage in rest of the face?

An injury where you describe can affect a branch of the facial nerve which controls elevation of the eyebrow.  This can cause heaviness and fullness. Sometimes this is not noticed until you get older because the brow begins to droop a little bit more and you don't have the ability to compensate by lifting it.  A brow lift and blepharoplasty can often help. An injury near your eyebrow would not explain the symptoms you are having on your lower face and lip.  There are a myriad of other causes for facial paralysis however. My recommendation is to seek a consultation with a neurologist to try to figure out why you're having those symptoms. Best wishes to you!

Thank you for the question.An eyebrow injury can potentially harm nerves that lift the forehead, eyelids, but typically does not affect the lips or areas below the brow. You may have something else going on, that may require you to first see you primary doctor with a referral to a specialist. Best of luck to you...

This suggests that perhaps something else is wrong or your assessment of what is going on is not right.  A photograph would be invaluable to actually understand what you mean. Please consider reposting with a face photograph so we can be more helpful.