I have no experience with this , here are a few suggestions.

Try to find a gallery that specializes in the textile medium.

I guess it would depend on the style or if a gallery was featuring like items. Did you create the pattern or is it a reproduction? From what I have seen galleries and museums exhibit items as part of a collection.

You may see if there are arts and crafts festivals in your area which often have juried (judged by experts)competitions who could talk to you about the quality of your work. Winning items are often displayed at festivals.

Local libraries often have display cases maybe suggest your item be displayed with books on embroidery.

Maybe a local sewing store that sells the type of floss you used would put it on display as an example of what could be done with the product.

Or contact the manufacturer of the floss maybe they would display it on their web site.

Any chance would share a picture with the afrigeneas crafters?