Possibly. It depends upon the causes of the rough landing.
Numerous circumstances can lead to a hard touchdown for a commercial jetliner. One particularly common cause is the weather, which may not, on its own, support a claim for damages. Airlines commonly limit their liability for weather-related incidents in the fine print you agree to when you buy a ticket.
However, airlines generally cannot escape liability for injuries caused by their own gross negligence or reckless misconduct. That may include making dangerous decisions about landing planes in unfavorable conditions, or ignoring warning signs from ground radars and other meteorological equipment. It may also include trying to cover-up a mechanical failure or pilot error by blaming a rough landing on weather conditions.
Speak with an attorney from The Levin Firm in Fort Lauderdale today about the injuries you suffered and the explanations (or lack thereof) that the airline gave you for what happened. You may have the right to compensation.