If I choose Jae Medarda with my own repeated Frigid Touch do I draw 2?

Yes, you draw 2 cards.

Here is the breakdown of why this interaction works this way:

1. Jae Medarda's Ability: Jae Medarda has the ability: "When you choose me with a spell, draw 1." This is a triggered ability that occurs whenever Jae is chosen as a target by a spell.
2. Frigid Touch with Repeat: When you play Frigid Touch with the Repeat cost, you are playing one spell that targets a unit twice.
3. Two Triggers: Because Repeat instructs you to "execute the effect of the spell one additional time," you are choosing Jae Medarda as a target for the initial effect and again as a target for the repeated effect.
4. Resolution: Each time you choose Jae Medarda as a target, her ability triggers. Since the ability triggers separately for each instance of being chosen, it will trigger twice.
   • First Trigger: You draw 1 card.
   • Second Trigger: You draw 1 card.

According to Rule 355.14.d, each target chosen contributes to triggered abilities individually. Because your Repeat allows you to execute the effect a second time, you are choosing your target twice, satisfying Jae's condition for each draw.