Is there a glitch in the program? I am trying to enter my claim period for medical expenses as Dec 11, 2019 to Dec 10, 2020 and it won't add my eligible medical expenses.

Only enter 2020 medical expenses on your 2020 return.  2019 go on 2019 return.  To get credit for medical expenses you must itemize deductions on Schedule A.  You will only get credit for medical expenses that exceed 7.5% of adjusted gross income.  You will only get the credit if you itemize.  You only itemize if your allowable expenses exceed your standard deduction.