If that were true, how come Apple computers have successfully trademarked their brand, all over the world inc. China? After all, you could argue that the word 'apple' has been around since Adam & Eve :lol:
If you saw Bluesky Coca Cola for sale in your local shop, would you expect it to taste the same as the real Coca Cola and be happy to pay a premium price for it?
Fair enough, if you're happy to use it on yourself, but it is a criminal offence in the UK to misrepresent a product or service to consumers, and clearly this is what happened to the original poster.
As has been said before, the Bluesky brand is clearly intended to con unsuspecting users by tradeing on an established brand name and for techs to use it, advertise it as Shellac and charge the same price as reputable Shellac users is clearly deception. If she had advertised the service as Bluesky Shellac, she might get away with it.
I would recommend that the original poster contacts the 'nail technician' and threatens to report her to her local trading standards unless she returns her money in full. Although, I think she should report her anyway as has been said before, it's quite possible that the product is unsafe.
Whilst not a Shellac user personally (prefer Gelish), I don't know any decent brands of Gel that smell awful, and that would ring very loud warning bells to me. (MMA anyone???)