As far as I know, there is no way to fix this by the Upwork's side. You shouldn't start any work without being hired previously, otherwise Upwork cannot guarantee that you will get paid.
Besides learning the lesson I guess what you can try now is to write to that client asking her to pay you so that you can guarantee her your services in the future (supposing she was satisfied with them).
PD: Before getting my first job in Odesk I made the same mistake too... don't worry, we all are humans.
I checked your account, unfortunately the client never offered an official contract with you. In the future, please do not start on any job until you are offered a contract, and it appears on the "My Jobs" section of your account when you have accepted it. If you think that during the interview process the client is already asking for work, report this client to our support team as it is a violation of the Upwork TOS to ask freelancers for free work.
You can not "fix" this.
You need to learn how to use Upwork properly.
When contractors volunteer to work for free like this, it drags the platform down for all of us, even the clients.
We can't expect clients to have a consistent, ironclad expectation that they will always pay for work while there are contractors who work for free.
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