I want to be clear that while I appreciate Shakespeare, a wonderful writer for both his and our times, I also connect as a believer with him. I believe your theologically grounded approach to love is genuine. Given that his writing falls under the category of "tragedy," a portion of his terrible ending has already been revealed.
Even while the Bible makes it very evident that love should not be egotistical, self-centered, or pursue evil, love may really develop into a possessive, unhealthy, and jealousy-inducing emotion as it grows toward someone. That doesn't mean it can't be love, though.