The PHB on p. 195 (or the corresponding section of the basic rules) says:
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
The rules do not make a distinction between “main-hand” and “off-hand” weapons.
My character dual wields a shortsword with her right hand and a dagger with her left hand.
Could my character attack with her left hand dagger first, doing 1d4 + STR/DEX mod damage, then attack with her right hand shortsword, doing 1d6 damage?
Does it matter which weapon I attack with first when two-weapon fighting?