mysql> create table DemoTable
(
   AdmissionDate varchar(50)
);
Query OK, 0 rows affected (0.63 sec)

mysql> insert into DemoTable values('15-Sep-2019');
Query OK, 1 row affected (0.19 sec)
mysql> insert into DemoTable values('14-Sep-2019');
Query OK, 1 row affected (0.10 sec)
mysql> insert into DemoTable values('13-Sep-2016');
Query OK, 1 row affected (0.15 sec)
mysql> insert into DemoTable values('13-Sep-2019');
Query OK, 1 row affected (0.11 sec)
mysql> insert into DemoTable values('13-Sep-2020');
Query OK, 1 row affected (0.10 sec)

mysql> select *from DemoTable;

+---------------+
| AdmissionDate |
+---------------+
| 15-Sep-2019   |
| 14-Sep-2019   |
| 13-Sep-2016   |
| 13-Sep-2019   |
| 13-Sep-2020   |
+---------------+
5 rows in set (0.00 sec)

mysql> select *from DemoTable where str_to_date(AdmissionDate,'%d-%b-%Y') < CURDATE();

+---------------+
| AdmissionDate |
+---------------+
| 13-Sep-2016   |
| 13-Sep-2019   |
+---------------+
2 rows in set (0.00 sec)