Yes, that would be illegal.
Copyright is often described as being a "bundle of sticks" with each stick being a different right. One of the sticks is distribution - so distribution of a copyrighted work may be infringement. One stick is the right to create derivative works - so making your own work derived from a copyrighted work may be infringement. Transcribing your cover was creating a derivative work from the original work. You likely won't run into any trouble if you keep the sheet music to yourself, but distributing it at all (especially for money) is a copyright violation and could result in some serious monetary damages for you.
This is not intended as legal advice. This does not create an attorney-client relationship.
Songwriters sell their "folio" sheet music rights along with their other rights in their "bundle," as apty described by my colleague, and it's likely that if this is a popoular song, it already has been published in sheet music form.
Copyright infringement depends on the substantial similarity of the original work and the allegedly infringing work, so if your version is "substantially similar" to the original, it's infringing. If it really is different, then it's not.
You've acknowledged acess to the work, in fact "covering" the song, which refers to a recording of an existing work. Courts don't look at access as much as they used to in evaluating copyright infringement, ut since you've acknowledged it, it could be a factor not in your favor. Your use of the original implies that your version is similar, prehaps substantially similar. But no lawyer can evaluate the degree of similarity without actually reviewing the works in question, so you should see your own music lawyer.
If the song is original enough to be registered for a copyright, published by a music pubisher, and registered with a Performing Rights Organization, then there's lots of paperwork to fill out to secure your rights.
If you're not prepared to hire a lawyer and want to take your chances by uploading your recording to YouTube, YouTube could get a DMCA "takedown" notice from the songwriter(s) of the song or their publisher(s), which will result in your recording being removed from YouTube, and it could also result in you being sued for copyright infringement. With copyright infringement statutory penalties being as much as $150,000 per infringed work, that's a pretty big risk to take.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
Under United States law, if you do not obtain a license from the copyright owner of the song, it is not legal for you to transcribe a new version or arrangement of the song (which is a violation of the right to reproduce the work and the right to prepare derivative works), nor is it legal for you to sell it (or distribute it for free) to the public (which is a violation of the public distribution right). Even if you have made changes to your "version" of the song, if it is recognizable as being based on the original it would require a license. Indeed, it would also be a copyright infringement for you to post a recording of yourself performing the song on Youtube (which would violate multiple of the exclusive rights under copyright).
It is also highly unlikely that you could own or legally register a copyright in your arrangement or version of the song (or register with a performing rights organization, etc.), because you created it without the authorization of the owner of the copyright in the underlying song.
Of course, these statements are based upon general principles, without examination of the actual works involved. You would need to have a qualified attorney examine the original song and your version to get solid legal advice you could rely upon.
Views expressed are mine and do not represent the views of Arent Fox LLP (or its partners, employees or clients) or the New York State Bar Association. This answer is provided for the purpose of furthering the analysis, understanding and discussion of copyright law. This answer is not an advertisement for my services, nor is it given for the purpose of soliciting my retention as your lawyer. Nothing in this answer is intended to serve as legal advice, nor should you rely upon this answer to serve as legal advice. If you need legal advice, please seek out and retain qualified legal counsel to provide such advice based upon your specific facts and circumstances. Nothing in this answer creates an attorney-client relationship with you. To be my client, you must be a client of my firm, which means that we must make certain disclosures to each other, check certain facts, make financial arrangements, and enter into a written agreement with and approved by my firm.