Absolutely no sugar syrup. It is dangerous for tiny little tummies and can make them dependent on artificial means of defecation for life.
When she's laying on her back, lift both legs near the knees and move her legs/hips in "bicycle" motion, circling as though she's riding a bike. This in addition to infant tummy massage works wonders on many babies.
Call your pediatrician to let them know of the situation and follow up if the massage and movement doesn't work.
Actually you want to contact her doc where she is so young. Also the mayo clinic advises against karo syrup, which is basically corn syrup, add the chemical make up has changed and is no longer effective. In any case at her age you want to update the pediatrician. When she's older, Prunes or prune juice works wonders. Infant tummy massage had been known to help keep things moving. You rub her tummy in slow movements clockwise around her abdomen. Good luck and congrats mama:)
Give her a little karo syrup in her formula because she is constipated. Its safe that is what I Gove my babies and it works like a charm. Just do a couple of spoons.