Had under eye filler and my dermatologist felt it had migrated. Hard lump under outer corner coming into mid eye area (Photo)

It very much sounds like there is retained filler.  I would get a second opinion, simply because often the wrong concentrations of hyaluronidase are being used. Dissolving fillers is actually quite specialised and it is often not done appropriately. It is also possible to get permanent lumps after filler injections resulting from granulomas and scarring reactions and these are more difficult to manage.

Most likely this result is due to improperly placed filler causing increased prominence of the fat pad and/or blockage of lymphatic drainage in this area causing fluid to accumulate.  Sometimes it can take several treatments with hyaluronidase to dissolve completely and get back to your baseline.  I would suggest once back to baseline to consider CO2 laser instead of filler as part of the issue is skin laxity which can be improved with this treatment.  Also make sure to use a quality eye cream as well.  kh

Although It is impossible to make any precise statements without an exam and more information, it appears that you simply had filler placed in the wrong place, above the orbital ligament. It is quite unlikely that the filler "migrated." The swelling looks like what we think is the result of clogging the lymphatics in the area, which is very common when filler is placed above the ligament. If it has not responded to hyaluronidase that will usually reverse the process, it probably will not and you will simply have to wait for its dissolution. Occasionally, mild massage from medial to lateral can help if this is the case.