As others have pointed out, for a home to appear on the local MLS, the home must be listed for sale by a member real estate professional.
Your question, "Can I make my own website for the listing?" would be a resounding YES...if it complies with the 'single purpose' use required by the MLS.
There may be real advantages in doing this, but none of those advantages are identified in your question. This may indicate that such advantages do not exist therefore may prove to be detrimental to your sale objectives.
Be aware, real buyers are not on Zillow or Trulia. Real buyers are using real tools. Your strategy may have more merit than others are acknowledging if you are an SEO expert and have access to the real tools prepared buyers are using.
So, in your specific situation...who knows what is best for you, .... there simply is not sufficient information.
Best of success to you,
Annette Lawrence, Broker/Associate
Remax Realtec Group