If there's fatigue in your arm to go along with this soreness after you play your tennis, the first thing that comes to mind for me is that you're using way too much arm to get the racquet to the ball. If you're using a proper setup and a sound "kinetic chain" to drive your shots, your arm shouldn't have too much work to do. Our stronger muscles are in our legs, but we don't always make the most of them when looking to take bigger swings.
A good indicator of how much oomph you can put into your strokes could be just taking some practice swings without hitting a ball. Take some reeeeally big swings and get in tune with the feel for how long it takes to execute that bigger stroke. That's your swing tempo. When you go out to hit balls, make sure you're getting set up and started into your bigger swings so that you can repeat that same tempo when a ball is coming your way. Otherwise, you'll be relying on the tempo for a shorter swing and your arm will have to rush the racquet to the ball. That's a sure recipe for soreness if you do too much of it.
