As for the "they could not be copyrighted thing", that depends on how much of the design you copied. If you took lots of elements from various other logos and blended them into something completely new, then there's a chance that you're not breaching copyright on those, but if it's too similar to any one logo then you've got a problem.
If you could post what you created here, along with your 'inspiration'/'reference material' we can tell you if it's alright or not.
A logo is a visual element that is/can be visually tied to a specific company, product, brand etc... you see the logo, and if it's successful, you recognise the brand associated with it automatically. It's a sort of memory aid to form a useful link in people's minds.
Logos can be art, they're not 2 separate things. If what i've described above is what you created, then it's a logo. Whether it's art or not is a subjective thing. Some might say yes, some might say no.
You would know yourself if the extent of copying that you're doing is wrong, so if you were aware that what you were doing was illegal, then i have no sympathy for you.
However, if you're not breaching copyright, then what you have is original, even if it's inspired from other sources. At the time you created that body of work, you automatically gain the copyright to it. It's not that something "Can't be copyrighted", you either have it, or you don't, simple as that. There's no register or organisation that keeps track of copyrights, just people that spot its infringement and laws that support those people.
As for the lack of contract, yes, chalk that up to experience but try to reason with her if possible to salvage at least partial payment. However, if you infringe on copyrighted material, then a contract would not help you in the slightest bit. It would only get you in trouble. But don't let fear of punishment be the thing that stops you from stealing, let it be some common sense, morality, ethics, decency and respect for the work of real designers, take your pick.
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Subtlety is my middle name... and first and last in case you didn't get the point.
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