It's going to be tough, but it might be possible.
Here is a rough summary of the three hurdles you need to clear.
The first hurdle is the NCAA 5-year time clock. It looks like you'll have one year available, so you're okay on that.
The second hurdle concerns what you accomplished academically at the JUCO. There are two different standards, depending on whether you were a "qualifier" out of high school.
--If you are a Qualifier, you have to graduate from the two-year college or average 12 transferable units of degree credit for each semester attended. (There's also a GPA rule, but you should be grandfathered out of that.)
--If you are a Non-Qualifier, you need to graduate from the two-year college, have at least 48 transferable units of degree credit (with certain amounts of English, Math, and Science), have a GPA of 2.50 in transferable units and pass 6 units in your last full-time term.
If you meet all these standards, you'll face the third and toughest hurdle for people in your situation: the "progress toward degree" rule. Assuming you were a full-time student for all the semesters you mentioned, you will need approximately 96 units toward a bachelors degree at your new school. It's very hard to meet this standard without a lot of upper level courses that are rarely offered at JUCO's, but you might be able to get there with prudently chosen courses in the summer and fall terms.
You might be interested to know that the "progress toward degree" rule would not apply if you transferred to a D2 school, so that may be an option you want to consider.
If you have specific questions you may send me a private dialog message.
Best wishes,