Should I be worried about light pink discharge in the first trimester?

Depends. If you have been sexually active or otherwise physically active, or had a recent cervical exam you may spot lightly. You also may have spotting related to a vaginal infection. As long as the spotting is not accompanied by cramps, severe pelvic pain, increasingly heavier bleeding or uncomfortable vaginal discharge, relax. If you have had a miscarriage or are at risk for an ectopic preg, contact doc.
GYN. It is not uncommon for a woman to experience spotting during the first trimester of pregnancy. Please tell your obstetrician. Take care.