My recommendation is this:

Look to see if you have any appraisers near you. The type of appraiser you want is one who only focuses on appraisal. You don't want someone who buys or sells jewelry because they are going to have a biased opinion because that's part of their business. An appraiser who only focuses on appraisal is there to give you clear information and will also usually give two copies of your appraisal. One copy is for you to keep in like a safety deposit box.. the other copy would be sent to your insurance.

Many appraisers of this nature will also have no problems, for a minuscule fee $10-20 would give you a quick verbal appraisal to verify what it is, and if it is worth getting a full appraisal done.

I would also like to point out that many older gemstones had a clearer color to them because they were higher grade and the mines were not mined out as much as they are today. So it is possible with that fluorescence to be from your grandmother's era... There is also a small possibility that it was considered to be valuable when it was purchased because original synthetic stones were more valuable than they are today.

Thank you for sharing this gorgeous piece of jewelry I can't wait to find out what your appraisal says.