MySQL - Make a pair of values unique

I have a table with two int values that are IDs. On their own these IDs can show up any number of times in the table, but together they should only ever appear once.

Is there a way to make a pair of values unique and still allow the individual values to show up multiple times?

As a follow up, if this is possible can the pair of values be used as a key? I currently have a 3rd column for a unique auto increment value for my key.

It's called a composite key.

If you want to change your actual PK to a composite one, use

Alter table <your table> drop PRIMARY KEY;
Alter table <your table> drop COLUMN <your autoincremented column>;

Alter table <your table> add [constraint <constraint name>] PRIMARY KEY (<col1>, <col2>);

You can also just add a unique constraint (your PK will be the same, and unique pairs... will have to be unique).

alter table <your table> add [constraint <constraint name>] unique index(<col1>, <col2>);

Personnally, I would recommend the second solution (simple PK + unique constraint), but that's just a personal point of view. You can google for pros and cons arguments about composite keys.

The part between [] are optional.

EDIT

If you wanna do this in the create table statement

For a composite pk

CREATE TABLE Test(
    id1 int NOT NULL, 
    id2 int NOT NULL,
    id3 int NOT NULL,
    PRIMARY KEY (id1, id2)
);

For an unique index

CREATE TABLE Test1(
    id1 int NOT NULL AUTO_INCREMENT, 
    id2 int NOT NULL,
    id3 int NOT NULL,
    PRIMARY KEY (id1),
    UNIQUE KEY (id2, id3)
);

Try this: ALTER TABLE table_name ADD CONSTRAINT uc_name UNIQUE (col1,col2)