Probably not: the open enrollment period for 2015 coverage ended in February. The open enrollment period for 2016 plans begins on November 1.
The Affordable Care Act doesn’t let people buy coverage year-round. If it it did, you could imagine people signing up - in the most extreme examples - in the ambulance on the way to the hospital. This would make premiums skyrocket, as people would buy coverage at the exact point when they were expecting incredibly high medical bills. To prevent that, Obamacare (and most plans you get at work, too) says you have to sign up in a certain time frame, and commit to buying coverage all year long.
There are exceptions to this rule. If you have a new baby, you’re allowed to have a special enrollment period; there’s no way said baby could have signed up before it was born. People who lose their jobs or move states can also shop for a new plan, even when open enrollment is closed. There are a handful of other exceptions, too, all listed here.