What you probably want to do is insert both directions in the friends relationship once both friends have confirmed. So instead of doing this:
INSERT INTO `users_friends` (user_id, friends_with) VALUES ('$user_id', '$username_id')
You would do this:
INSERT INTO `users_friends` (user_id, friends_with) VALUES ('$user_id', '$username_id'),('$username_id','$user_id')
This would allow you to do the friend lookup in either direction.
What is unclear to me however is how you store pending friend requests in your database. So what you may ultimately need to do is to insert those relations in the DB and then simply update those DB records to change the value of an "accepted" flag once the friendship has confirmed.