Comparing two dates (Formatted Date as a String and Current Time) using before method

I need to use the before method in Java. So I can do date compare code like this:

if (storedDate.before(currentMonth)) {

}

Where currentMonth is set like this:

int thisMonth = Calendar.getInstance().get(Calendar.MONTH) + 1;
cal = Calendar.getInstance(); df = new SimpleDateFormat("MMM yyyy", Locale.ENGLISH);
cal.set(Calendar.MONTH, thisMonth);
// Do I even need to convert like this to match what is stored in the DB below?

And storedDate loops through a SQLite table where dates are stored as formatted Strings such as "Nov 2013" or "Dec 2014"; yes, bad design I know.

What I need to do is see if the date in the current row in the loop is older than this month; if so, I will delete it out of the SQLite DB (I have that code which is fine).

So, how can I build the two variables where I can compare like this if (storedDate.before(currentMonth)) {?

EDIT:

This is how the month is stored into the DB:

            monthTotal = monthTotal + 1;

            Calendar myDate = Calendar.getInstance();
            myDate.add(Calendar.MONTH, monthTotal);

            SimpleDateFormat dfEng = new SimpleDateFormat("MMM yyyy", Locale.ENGLISH);
            String finalDBDate = dfEng.format(myDate.getTime());

EDIT2:

Here is what I have so far

private void deleteOldSpecialPayments() {

    int thisMonth = Calendar.getInstance().get(Calendar.MONTH) + 1;
    cal = Calendar.getInstance();
    df = new SimpleDateFormat("MMM yyyy", Locale.ENGLISH);
    cal.set(Calendar.MONTH, thisMonth);

    String thisMonthS = df.format(cal.getTime());
    Date currentDate = null;
    try {
        currentDate = df.parse(thisMonthS);
    } catch (ParseException e) {
        e.printStackTrace();
    }

    if (!database.isOpen()) {
        open();
    }

    Cursor cursor = database.query(MySQLiteHelper.TABLE_CUSTOM_PAYMENTS, allLedgerColumns, null, null, null, null, null);
    cursor.moveToFirst();
    while (!cursor.isAfterLast()) {
        SpecialPayment sp = cursorToCustomPayments(cursor);
        try {
            Date d = df.parse(sp.month);
            if (d.before(currentDate)) {
                // DELETE ROW
            }
        } catch (ParseException e) {
            e.printStackTrace();
        }

        cursor.moveToNext();
    }
    // Make sure to close the cursor
    cursor.close();
}