The standard phrase or idiom is tug at one's heartstrings:
one's heartstrings
used in reference to one's deepest feelings of love or compassion:
the kitten's pitiful little squeak tugged at her heartstrings
Also, NOAD defines tug thus:
pull (something) hard or suddenly
Thus, when something tugs at (pulls at) your heartstrings, it deeply affects your feelings in some way (a prick, a pang, etc).