There is no such thing as "DREAM" Act since that proposed legislation never cleared Congress. There is only DACA which is nothing more than a 2 year "Deferment" of deportation, with a work permit as a bonus. You seem to qualify for DACA based on the facts you cite. I strongly recommend that you file with the help of an experienced immigration attorney in Chicago.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
If the program you completed was accredited, it should be sufficient to prove you completed high school. Before applying, you should meet with an attorney to make sure there are no other issues that could derail your plans. There are plenty of immigration attorneys in Chicago, many of whom provide free consultations.
It appears that Pennfoster is accredited ... you should be OK for the DACA program ... there is no DREAM act.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.