This is something you should document. In some way that time stamps the phone calls if you can, in writing in your own words if not. If there are messages where the douchebag actually says your job is in jeopardy because you used a sick day, make a copy of that thing and put it in a vault somewhere, because that's gold (literal gold in a wrongful termination suit). This is an actionable complaint that brushes up against FMLA protections that you can take to HR, and your manager will get in deep shit. Your sick time, so long as the company gives you sick days, is your sick time.
I realize actually doing this is not as simple as all that, since managers and even smaller companies will make an employee's life hell if they actually exercise their rights as workers. So I'm not exactly saying complain. But document and keep, because it'll probably happen again in a circumstance where letting it go isn't an option.