If I accidentally spilled water on a customer’s daughter, can they sue me for emotional damage?

I accidentally spilled water on a customer's daughter while carrying a tray of 5 drinks (all ice waters). She bumped into my elbow and one of the plastic cups tipped over on the tray and spilled water down her back. She was younger so she started crying. I rushed to get towels and asked if there was anything I could do to help. My manager said the food would be on the house in compensation for the accident. The guy said he would sue for emotional damage and he took down our insurance's contact info.