A letter from of recommendation from your current learning institute in Singapore and a letter from the American University stating that you do not require a high school diploma to attend should be sufficient enough. I would also inquire at the consult to see if this would be okay. Maybe taking relevant tests and exams is an option also.

Bear in mind however a visa request is granted or declined at the Consult’s discretion.

Edit: Based on your additional information, the equivalent to a high school diploma is a GED (General Education Develoment) see below for more details.

http://en.wikipedia.org/wiki/General_Educational_Development

If you are not interested in going back to school for what ever reasons, may I suggest that you try and find an online course from an accredited learning institution, this way you can learn and complete the course in the comfort of your own home.

I would also take the steps that Ben and myself suggested to you earlier regarding contacting the embassy, the English centre in the states and your current school in Singapore.