How do I use SELECT LAST_INSERT_ID() without closing the connection

Question

I have table whose only column is an auto-incrementing primary key. I want to insert a new row into this table, and then get the ID generated by this insert.

Reading through StackOverflow, LAST_INSERT_ID() appears to be the standard solution. The caveat given is that it will return the last generated ID per connection. I wrote a new method to INSERT and then SELECT, all without closing the connection. Then I started getting "Operation not allowed after ResultSet closed" errors. Reading up on that in StackOverflow leads me to think I should not be preparing multiple statements on the same connection.

How should I be implementing this insert and select model? Am I misunderstanding what counts as the database connection concerning LAST_INSERT_ID()?

relevant excerpts:

public class ConceptPortal {   

    public static ConceptID createNewConceptID() throws Exception {
        ConceptID returnConceptID = null;
        StringBuilder stmt = new StringBuilder("INSERT INTO " + MysqlDefs.CONCEPT_TABLE + " VALUES ()");
        ArrayList<Object> parameters = new ArrayList<Object>();
        StringBuilder stmt2 = new StringBuilder("SELECT LAST_INSERT_ID()");     
        ResultSet resultSet = MysqlPortal.specialExecuteStatement(stmt.toString(), parameters, stmt2.toString());
        if (resultSet.next()) {
            returnConceptID = new ConceptID(resultSet.getLong(1));           
            resultSet.getStatement().close();
        } else {
            throw new Exception("Wait a minute...I can't create new concepts?!!");
        }
        return returnConceptID;
    }
}



public class MysqlPortal {
    private static ConnPool connPool = null;

    public static void init(String database, boolean startFromScratch) throws Exception {
        databaseName = database;
        connPool = new ConnPool(database);
    }

    /*
     * This one doesn't close right away,
     * so that we can run LAST_INSERT_ID() on it
     */
    static ResultSet specialExecuteStatement(String sqlCommand, ArrayList<Object> parameters, String followUpSelect) throws Exception {
        ResultSet resultSet = null;
        if (parameters == null) {
            System.out.println(sqlCommand + " :: [null]");          
        } else {
            System.out.println(sqlCommand + " :: " + Arrays.deepToString(parameters.toArray()) );
        }

        ConnectionImpl connInstance = connPool.aquire();
        try {
            Connection myConn = connInstance.getConnection();
            try (PreparedStatement pstmt = myConn.prepareStatement(sqlCommand)) {
                if (parameters != null) {
                    int i = 1;
                    for (Object parameter : parameters) {
                        pstmt.setObject(i, parameter);
                        i++;
                    }
                }
                pstmt.execute();
            }
            try (PreparedStatement pstmt2 = myConn.prepareStatement(followUpSelect)) {
                resultSet = pstmt2.executeQuery();
            }

            connPool.release(connInstance);
            return resultSet;
        } catch (SQLException e) {
            System.out.println(sqlCommand);
            throw e;
        }
    }
}