It is important to see a specialist (oculoplastics) for filler injection in the upper eyelid/brow area. It is a very safe procedure when done correctly. Also, best to use a soft hyaluronic acid gel filler such Belotero. See link below.
Non-surgical treatment of sub mental fat or "double-chin" can be performed with Kybella (deoxycholic acid) injections. It is only approved for sub mental fat, not face fat. Its the old mesotherapy that has very questionable history and in my opinion should never have been approved by FDA but it...
There are no known cross-reactivities with NSAIDs and any of the fillers. You should be ok to proceed with injections. However, be sure to have a thorough discussion with your physician prior to treatment.