I would think you should use a flutter kick - to get there.
I would practice snorkeling with the jet fins and try to do several fast 50 yard swims in the pool. this should improve your technique and will result in strengthening eventually. Breathing from the snorkel.
Then (on the same day) I would practice the breathhold stuff - with a partner. First let yourself calm down and relax after the 50's. Then wear a weight belt and just do some static breathholds on the bottom with no mask. You should be able to do 45 seconds or so without trying. maybe 3-4 with a good 2 minute rest between. Don't push it, just see what you can do with only very slight uncomfortableness.
Then with a mask and snorkel and the fins, just do some casual surface swims with a relaxed flutter kick and no breathing. Try to swim gently and just see how far you get. 25 yards really should not be that hard. Again, don't push hard, just see how far you can get with maybe 80% effort. After you master 25 yards several times, you will feel better. It is not hard.
Do that work out 2-3 times in a week and you should be in better shape and way more confident and relaxed.
I would not believe anyone who tells you that you have another 2 minutes of apnea before you pass out (after you feel urgent need to breathe). If you feel bad come up! Don't hyperventilate, but taking 2-3 deep inhalations and exhalations before the dive should help.
A good bit of the apnea performance is psychological and the feedback you get from your body. If you have not adapted to the stress of breathhold, you will get panicky, you will flex muscles that should be relaxed, your brain will race and burn more oxygen (DO NOT discount this effect). You really want your breathhold (apnea) to be, for the most part a comfortable and relaxed activity - not something super stressful and difficult like lifting a heavy weight in the gym. You want to be saying to yourself (internal dialog).. I feel fine, I'm good, I'm relaxed, I'm moving gracefully and efficiently. NOT "I think I'm going to die!"
If you have normal physiology, your battle is within your brain and also making sure your kick is efficient and reasonably powerful and 15 meters should be very attainable.