Sorting by date from bad string field in SQLite?

I'm using an SQLite database in an app I'm developing with ionic, but unfortunately the database is built in such a way that the date fields are strings, not proper Date type values. (I'm not the person who's responsible for building this database, nor can I ask them to fix this). They all follow a "DD-Mon" format.

So the structure is as follows

id  |date    | (other columns...) 
1   |"25-Jan"|
2   |"25-Jan"|
3   |"30-Jan"|
4   |"30-Jan"|
5   |"31-Jan"|
6   |"31-Jan"|
7   |"31-Jan"|
8   |"31-Jan"|
#   (500 more rows like this)

The problem is that I want to use a query that only gets the dates from a certain day onwards (something like SELECT * FROM table WHERE /*(date after X)*/;)

One thing to notice that might be helpful, although I still couldn't think of a solution, is that the IDs go from early to late, so if a given id X is greater than an id Y, then date X comes after date Y.