Travelers flying the busy route between Washington's National Airport and New York's LaGuardia Airport next month will find fares higher on both Eastern Airline's Air-Shuttle and New York Air's competitive service.

At the same time, the winter fare war on flights to Florida continued yesterday when Air Florida dropped its ticket price from $114 to $107 each way Monday through Thursday and from $135 to $127 Friday through Sunday. The new fares go into effect next Wednesday. Other airlines said they will match Air Florida and wondered what will happen next. "We'll see what the dawn will bring," an Eastern spokesman said.

On the Washington-New York route, New York Air said it will raise its regular one-way weekday fare from $49 to $55 next Wednesday. The airline, which began to challenge Eastern's near-monopoly on the route a year ago, said its weekend fare also will rise by $6 to $35 each way. The fare increases are the first since New York Air started service on Dec. 19, 1980.

Eastern said it will raise its regular fare for the 215-mile trip from $59 to $60 each way on Jan. 11. The fare on the shuttle had been $60 from May 1980 until October 1980, then there was a $1 drop in a federal tax, and the fare was reduced. Eastern also said it will raise its $29 special weekend fare to $35. Introduced last December to match New York Air's, Eastern's weekend fare is good on its flights between noon Saturday and noon Sunday.

Eastern also said it will raise its weekday shuttle fare from New York to Boston from $49 to $55 and its special weekend fare by $6 to $35. New York Air dropped its Boston-New York flights on Dec. 1.

New York Air President Neal Meehan yesterday attributed the fare increases to escalating costs. "We've been in the market over a year now with the same fare," he said. "Our hope is to hold the fare level through the remainder of the year." He said that New York Air's $35 weekend fare is still the lowest unrestricted fare in the market. "We're still quite lower than what the existing fare was prior to the entry of New York Air," he said.

A spokeswoman for Eastern said yesterday that, even with the fare $1 more, the shuttle is "still a bargain." She said that because of increased fuel and other costs, other domestic fares have gone up by an average of 16 percent since May 1980 while the shuttle fare remained stable. She also noted that the allowable fare between Washington and New York, set by the Civil Aeronautics Board, is $110.

Since New York Air arrived on the scene, it has stimulated passenger traffic in the Washington-New York market and has captured between 25 and 30 percent of the total, Meehan said. At the same time, the number of passengers traveling on Eastern's two shuttle routes--between Washington and New York and New York and Boston--has increased about 1 percent, an Eastern spokesman said. The Washington-New York route represents about two-thirds of Eastern's total shuttle business.

In another development, Air Jamaica said it will begin nonstop service from Baltimore/Washington International Airport to Montego Bay, Jamaica, on Feb. 19. The airline will offer flights on Fridays, Saturdays and Mondays with a special round-trip fare of $250 through April 15. The new service will add significantly to the Washington area's nonstop access to warm, sunny places in winter. With the exception of service to Puerto Rico, there are few direct flights to the Caribbean from Washington airports.

Air Jamaica doesn't have a Washington-area phone number yet but will take reservations through its Philadelphia office.