Hurricane season is June 1-November 30. No one can predict when, where, how often or at what level hurricanes will be. There might not be any hurricanes that affect Harlingen, there could be one and then none for years, there could be hurricanes every year. Experts make predictions before the start of hurricane season, and then we all wait and watch to see what happens.
You could do a google search to see the history of hurricane activity that has affected Harlingen and the south Texas coast, but that doesn't help you predict the future.
See if this web site will offer you any help: www.srh.noaa.gov/bro/?n=hurrprep_history (For what it's worth, Harlingen is in Cameron Country.) As TxOffWeGo said, past history is not an accurate predictor of the future.
For what it's worth, I've lived in Houston over 70 years, and I'd guess we've probably average about one hurricane about every 10-12 years here, and we're only 50 miles inland from Galveston. While they're no fun to live through, we get plenty of warning nowadays, so if that's the only thing keeping you from moving to Harlingen, odds are that you won't see very many of them.