It's probably normal. I teach surf preparation cardio workouts (paddling on a lake) and beginners are usually wrecked at the end of the lesson and it doesn't matter at all whether they do strengh training.
Before your next trip, do some surf-paddling first. That's the best preparation for surfing. Front crawl (as mentioned in the other answer) works if you happen to be good at it or want to train swimming anyway, but paddling training is much more focused on surfing and provides additional benefits over swimming.
Just take your surf board into a lake or river and do a cardio paddle workout on it with some high intensity intervals.
Basics: Press legs together, keeps legs over center of board, lift up shoulders, lift up feet if possible (and lift knees too if possible). Nose of board right at the water line. Neither the board nor your body wobbles or turns side to side while paddling.
Good exercises which I use in my training, ordered from basic to more advanced:
- sit up on board, don't press your knees against it, you just loosely sit on it
- while sitting up on the board, lift your hands to shoulder height and turn from side to side while keeping your arms in front of you
- while sitting up, board flat, turn with just your feet as fast as possible
- while sitting up, nose of board around 45 degrees up, turn with just your hand. One hand grips the side of the board, the other pushes water away from the board in a circle. Most beginners splash the water back - but you are neither supposed to splash, nor to go back. Your hand moves in as large of a circle as possible and not so explosively that you splash, that would be useless
- while sitting up, nose up, do turns with hand and feet
- paddle, single narrow push-up on knees, paddle
- paddle, sit up, lay down, paddle
- sit up, then start sprinting, quickly laying down in the right position on the board
- get off the board, lay arms over the board and grab your feet on the other side of the board. Very relaxing between hard exercises
- alternate for 10-20 strokes each: 1) good position, shoulders up as far as possible, move to the front of the board a bit so its nose is just at the water line. Really work your shoulders here. 2) bad position, shoulders down, you need to move back a bit so the board's nose doesn't dive below the water line. Yes, using intentionally bad form in the recovery phase is good here.
- paddle, 360 turn, paddle
- sprint, 180 turn, sprint
- alternate paddling techniques for 20 strokes each: front crawl style with elbows high and surf style with extended arms swinging forwards. Front crawl style is more suited to sprints, the other for distance.
- focus on grabbing a packet of water at the front and then pushing it as far back as possible with each stroke. Don't splash.
- sprint interval with focus on left/right hand movement, if you feel your hand slipping through the water too much with not enough resistance, do an S with each hand during the pull.
- pair up with someone else. Partner A closes eyes and paddles, partner B helps them to stay on a straight course by giving left/right instructions. Then switch. You can extend that with more possible instructions like left/right commands not aimed at going straight or blind 180 turns.
- turtle rolls, i.e. roll sideways into the water, turning your board on top of you. Stay down for a couple of seconds. Then roll up again.
- duck dives, i.e. sprint, make the board dive into the water and then follow the board. Only possible with boards that are likely too small for beginners. Best to watch some videos.
- sprint, then duck dive or turtle roll, sprint. Repeat with some active recovery in between
- many combinations of sprint, duck dive, turtle roll, 180 turn, 360 turn.
- paddle with both hands synchronously for 10-20 strokes
- do zigs and zags while lying down, i.e. change your direction abruptly by 30 to 45 degrees.
- sit up on the board and put your legs in front of you on the board. More difficult: Cross legged, or without using hands to keep balance.
- find a comfortable position on the board where you aren't straining your shoulders too much. Start paddling and every 5 to 10 strokes move forward 1-2 cm. Repeat until you fall of the board. This will make you lift your shoulders high to stay on the board as long as possible.
(this list kind of went on and on and still doesn't include every exercise I like to do. I didn't realize before that I use this many different exercises)
And of course don't forget normal interval/endurance training.
If you do this a couple of times per week for a couple of months before your surf trip, you will be able to surf all day, every day.