Medicare retroactive coverage?

You don't need health insurance to get treated for an ear infection.  You could probably get a place like MinuteClinic to give you a prescription for under $100.

No, it is not true.  Your friend is delusional.  You need to buy medical insurance to cover the gap between mid Dec and when your new plan starts.

Medi-Cal CAN BE retroactive when you have a serious medical condition.

A painful ear infection that would cost about $58 to be seen at minute clinic and get the related antibiotics does not qualify.

= you don't need health insurance to cover a minor cost like this.  If you don't have the $50-$100 to be seen at a place like minute clinic, go to a income based medical clinic.  Without knowing where in CA you are, it's difficult to provide information.  in Los Angeles, Harbor UCLA Medical Center has one.

Serious = tens of thousands of dollars in medical bills.

I think you mean medicaid, not medicare.  Medicaid will cover bills up to 3 months prior to your application date.

If you are not 65 or older or have a disability that allows a younger person to qualify for Medicare, you cannot enroll in Medicare.  You may qualify for Medicaid, which has 3 months retroactivity from the date you apply.