We're glad to have you! Also, glad to hear you enjoyed/are enjoying DAI!
You should absolutely play the previous two when you get some free time - just remember to go into each knowing that not a one of the three DA games plays like the others. DA:O is a bit more clunky, but the story is phenomenal. DA2 is faster paced, but the story-telling is a framed narrative, a re-telling you're getting to shape, rather then a "happening now". The protag is named and voiced - like with DAI, but Hawke is more a reluctant anti-hero then a "Successfully save/intentionally wreck the everything" type.
If you go into each game with that knowledge, you'll find yourself being able to enjoy each for what they are - Separate stories of separate people set in the same universe, during the same general time period: Aka, The Dragon Age.
If you do plan on going back, I'd normally suggest playing 2 first, but since you've started with DA:I, go with Origins. That way once you get to 2, you'll (at least I always am) be grateful for the much faster pace of the combat.