Is a non-accredeted Petroleum Engineering major still worth it ?

The choice of school would seem to be the least of your worries. Have you not gotten the memo? Oil prices have crashed, and so has the industry. And Iran is about to further flood the market with another million barrels per day. I can hardly think of a riskier subject to major in now.

FYI:
Is There Money to Be Made in Oil? New Grads Don’t Think So
http://www.bloomberg.com/news/articles/2015-01-29/graduates-question-six-figure-oil-jobs-as-layoffs-swell

Who Will Hire a Petroleum Engineer Now?
http://www.wsj.com/articles/who-will-hire-a-petroleum-engineer-now-1431130173

Oil Firms Face Reality of Sustained Low Prices
http://www.wsj.com/articles/oil-companies-face-reality-of-sustained-low-prices-1446124922
(If you don’t have a subscription to the WSJ, you can read the article for free by Googling its title. )

And don’t count on getting a job outside the US:
From Venezuela to Iraq to Russia, Oil Price Drops Raise Fears of Unrest
http://www.nytimes.com/2015/08/25/world/from-venezuela-to-iraq-to-russia-oil-price-drops-raise-fears-of-unrest.html?_r=0

The Gulf States are now in the unfamiliar situation of having to borrow money to stay afloat.