In answer to your question: What should I do with it to be fair with myself and my academic institution?

1. Review your academic institutions policies. You don't want to do anything that violates the rules.
2. You should never, ever submit the model paper as your own. In your word processing program, open two windows - one with the model paper, the other with your own research and writing. Your own window will start as blank. Do not copy the parts of the model paper - you must read it first, then think about it, and come to your own conclusions. If you have more questions, do more of your own research. Go through each paragraph and by the time you finish, you should have your own paper written using your own words.
3. Cite the model paper in the References section of your paper. Don't be afraid to use the website's address that helped you; it's not illegal to use academic paper research notes.
4. Read the paper you wrote again and try to remember the most important points in case your professor asks you about the details. It should be an easy process since you have done most of the research work yourself.
5. Once your paper is graded, read your professor's comments carefully. What have you missed, what could be improved? Read the model paper and your own paper again and remember the parts that were done correctly. The most important thing is that you actually learn something from the research and this knowledge will be useful when you write your next paper.
Good luck!