J1 internship Jun-Sept followed by H1b in October possible?

[jerrymazda]

I have an internship offer from june to september from company A and a full-time offer starting in october from company B. Am I allowed to apply for both visas almost simultaneously? I am aware that after the J-1 I have to return to my country and can't stay in the US. I believe the two-year rule also doesn't apply to me because the internship is paid fully by the company I'm working for, with no help from any government. Will my previous J-1 negatively affect the process for getting a h1b?

Many thanks in advance for your replies!