Probably a good idea. GIA or AGL would be my recommendation.
I have some beryl crystals from Nigerian that straddle the line between green-blue aqua and blue-green emerald (just as your stones appear to me in the above photos). There may be some professional differences of opinion on your stones.
I’m not certain, but it might be something along the same lines as when do you call a pinkish corundum “ruby” rather than “pink sapphire”. The jokes goes: “it’s pink corundum if you’re the buyer and ruby if you’re the seller”! There’s no definitive distinction from chemical composition or testing standpoint.
In the past, it was thought that emeralds had to be colored by chromium, but (if I recall correctly), most African emeralds are colored by Vanadium.
My guess is that your stones are Nigerian in origin, and it might be a roll of the dice as to whether the cert comes back emerald, aqua, or possibly even “green beryl”.
Keep us updated please!