You are presenting multiple issues; let's address the fundamental issues first, and then maybe the other will resolve.
the government is claiming taxes for the complete amount she billed the client throughout the period we worked
This does not sound like the tax return was filed correctly. Regardless of the business status (Sole Proprietor, LLC, Sub-S corp, etc.), the expenses of the business, which would include outsourced work
, should have been included in the return. Just guessing, but this sounds like someone issued her a 1099 for the entire amount, but she did not claim the amount she paid you as income, and either failed to file the proper forms, or supporting documentation. The amount of money involved might also have something to do with it.
she needs to find a way to deduct the money she paid me
Every month, I sent her an invoice
That's the way she can deduct the money she paid you as a business expense.
Your friend might want to consult a competent local accountant to review her situation, the recently filed tax return, and help her deal with this issue. This seems to be a fairly basic issue, based on what is stated here, and could probably be resolved with an amended filing. The accountant will be the definitive source of advice re that.
At the same time, that accountant could probably advise on your personal tax issues. I am presuming that would not be imposing, since you are friends. That type of advice is best received from a financial and tax professional.