Nipple pain... Could this be related to breast implants?

It is highly unlikely that breast implants will cause nipple pain after the operation. This is a situation you should report to your plastic surgeon.

There are a couple of pieces to the puzzle that you have left out here, and that information would be very helpful in figuring out what is going on.  You didn't say whether the pain or sensitivity are new things over the past couple of months, or they were there all along and it increased during this time.  In addition, you didn't tell us whether the lumpy tissue under the nipples was there all along or it has increased or suddenly appeared.  These are important considerations and can help guide a diagnosis.  Most of the time these things represent scar tissue resulting from the surgery, not necessarily the implants themselves, especially if a periareolar incision was used, and nerves can be involved in the scar tissue leading to chronic sensory changes and pain.  The bottom line is that you should be evaluated by your surgeon, and this should include a mammogram at the very least if you haven't already had one.  When you go to see your doctor, be sure you are armed with as much specific information about time course and severity of any symptoms and findings as I have outlined above. That will help him or her zero in on what is going on.  Good luck.