Well, I think it's a rumor, but I just looked up that she got tested and she as negative. Here's an article:
Jamie Lynn Spears looks like a miniature version of her big sister Britney – and she’s starting to act like her too. Jamie Lynn recently suspected that she was about to become a young mother herself, though at 16, she’s several years younger than Britney was when she had her first child.
According to Australian tabloid NW, Jamie Lynn believed she was pregnant with her boyfriend Casey Aldridge’s child earlier this month. Worried about her future, Jamie Lynn turned to Britney for help. An insider tells NW, "Britney told Jamie Lynn she'd help her with anything she needed. She promised to keep her secret and not say anything."
Of course, Britney’s estranged mother Lynne was not pleased that her younger daughter was turning to her older one. She took Jamie Lynn out of Britney’s influence and back to Louisiana where Jamie Lynn took several pregnancy tests.
Luckily, the results were negative, but, one source says, "This whole pregnancy scare has really stressed Lynne out.” Another snitch agreed, stating, “[Lynne] sees Jamie Lynn as a rising star, a protégée to Britney who'll go on to a big career. Now, she's worried Jamie Lynn's trashing herself, turning into a carbon copy of her big sister. [The pregnancy] could wreck [her] career."