Is there a way I can see which cards I have Shared and which have been Shared with me in the past?

You can view your Share history through the following steps.

■Steps to check which cards you've Shared:
Tap Social Hub (middle button at the bottom of the screen) > Share > History.
You can confirm up to your last 30 Shares from the past 90 days here.

■Steps to check which cards have been Shared with you:
Tap Home Screen (leftmost button at the bottom of the screen) > Gifts > Claim/Claimed.
You can confirm up to the last 100 items you've claimed from the past 30 days here.