despeque, don't simply write the word 'wrong' simply because you hope I am wrong. Do some research. You will be found out and you will pay the unpaid tax, the penalty and maybe a fine, no matter what you think.
The bilateral agreement means that you will not pay tax in BOTH countries, only in one. The agreement means that the country where you are from/born/previously worked, relinquishes the right to tax you, as you are no longer resident, on the understanding that you pay tax in the country where you now live and work. It most certainly does not mean that you are exempt from paying tax somewhere! No-one is.
It does not state, nor can you interpret it any other way, that if your employer is in one country and you are living and working in another, maybe paid by an agency or even to you as a limited company that you need not pay tax somewhere.
I say again, it is your responsibility to inform the local tax office of your emplyment, wherever you work, wherever your employer is based.
The excuse of ignorance of the law is not a defense. Try it when you get caught in the net. It does not work. Trust me!
The most sensible thing for you and all the others in a similar situation is to get an accountant and register for tax, soon.
I am very touched by your story about how much money you have spent on your education and training, as will be the tax authorities similarly touched. Sorry, you have to pay, just like everyone else. Sympathy doesn't reduce your tax bill though.
As I wrote elsewhere:
There is a very easy way to tell if you are liable for tax.
Ask yourself this simple question; am I happy for the tax authorities in the country where I now live and work to know all about my financial arrangements?
If you answer NO, then you are breaking the law in that country.
It really is that simple.............get real