设置多个唯一约束

I'm trying to set unique contraints for multiple columns in the database for my WordPress plugin. I have seen many answers to similar questions here on Stack, but I'm unable to make it work in my context. I followed the WordPress documentation for Creating Tables with Plugins.

I have tried

CREATE TABLE media (
    id mediumint(9) NOT NULL AUTO_INCREMENT,
    name tinytext NOT NULL,
    email VARCHAR(100) NOT NULL,
    CONSTRAINT mediaID UNIQUE (id, email)
) $charset_collate;

and

CREATE TABLE media (
        id mediumint(9) NOT NULL AUTO_INCREMENT,
        name tinytext NOT NULL,
        email VARCHAR(100) NOT NULL,
        UNIQUE KEY id (id)
    ) $charset_collate;
ALTER TABLE media
    ADD UNIQUE (email)

Unfortunately non of these works, as I'm able to add two records with same email address. I have tried to enter "ALTER TABLE..." manually into phpMyAdmin, and then it works. But not in the plugin code.