No, the points will not show up on your New York driver's license for a conviction of a Florida speeding ticket.

Both Florida and your home state of New York are members a reciprocal agreement named the Drivers License Compact (DLC) which means that the FL courts will inform the NYS Department of Motor Vehicles about the Florida speeding citation. However the NYS DMV states that they do not record out-of-state violations committed by NYS drivers in other jurisdictions, with a few exceptions.

The exceptions are alcohol-related violations, drug-related violations, and moving violations committed in Quebec or Ontario. Under special agreements, traffic convictions in Quebec or Ontario are recorded on NYS driver license records and carry points. Except for violations in Ontario and Quebec, points are not added to your New York license for out-of-state violations.