Extremely concerned about employment background check

I recently landed my dream job, and part of the process is a background check that includes employment verification. I had an internship for 2 summers at a Fortune 500 company, but the second summer, had to leave after less than 2 weeks due to a health issue. I made the mistake of leaving early one day because I wasn’t feeling well at all, and because the internship was hourly, I figured I’d just enter my short hours for that day.

Obviously, that was a terrible decision and it ended up being an issue with my boss and HR, who seemed to be assuming I was trying to fudge my hours. I resigned the day after citing my health issues (which I was going to do anyway), and proceeded to get a couple of surgeries to rectify things.

My concern is that because these internships were at the same company, when the new employer attempts to verify my employment, they will see that I was at the old company for less than 2 weeks last summer. This will obviously lead to questions, and they may ask to speak to my former boss to verify that I left due to health issues. I am extremely worried about what else my boss might say - specifically about leaving early. Does anyone have advice as to what I should do?