It might be the soap gel you mentioned. I used to always use a cleanser on my face, but it always seemed to dry my skin really bad. I've stopped using cleansers for around 5 months now and my face isn't as oily! It gets oily but it's due to temperature around me. Anyways, you could always stop using cleansers for awhile to see if it makes any difference. I just clean my face warm water, then cold water - twice a day. only clean your face with water more than twice if you're sweating from a workout. Other than that, if you feel it's too oily, pat dry with paper. (Blotting and tissue paper work best) I think this should help you alot. Give it a month and see if you notice any difference!
I think you should take antibiotics but in moderation. Don't take it for too long and try to get probiotics aswell once you're done with antibiotics to get back the 'good germs' in your body that help protect you from diseases, infections, etc. And it is normal for teenagers around your age to begin puberty and getting acne. It's probably mild, anyways. Don't stress over it, it happens.
Masturbation has nothing to do with acne. It is actually good for the body, because it helps your hormones balance and reduces stress-levels. It's a coincidence that you stopped having breakouts, but masturbation isn't the cause. And the redness might be from various reasons, cold, heat, what you ate, forcing your body too much, etc.
First thing you should do is try to minimize washing your face to just twice a day. Washing more than twice can overdry.
Second thing, get enough sleep if possible. Try to aim for 8 hours, though the amount of hours varies per person.
Third thing, drink more water. Aim for 2 liters+ a day (8 glasses), it doesn't have to be all at once, but just drink that throughout the day.
Fourth thing, diet: instead of sugary drinks like sodas, juices, etc. replace it with water. If you want drink green tea with NO caffeine, it has many antioxidants. Stay away from dairy for a while to see if you see any difference. Eat vegetables and fruits to get your daily vitamins. If you can't get those daily, get multi-vitamins.
Fifth thing, don't touch your face. It's hard to do, but stop yourself from doing it as much as you can.
Sixth thing, masturbation has NOTHING to do with acne. It's actually healthy for the body and balances your hormones & stress levels. Just don't over-do it, lol.
Last thing, stay positive. You're still young. Hormones get wild when you're in the stage of puberty, in a few years (or less), it will stabilize and you'll have less acne breakouts.
Care for your skin!
I know you mentioned you've tried Neutrogena but have you tried the Nuetrogena oil-free moisture with Sunscreen SPF 15? It only has three active ingredients & it has never broken me out. You can also look up reviews and people agree that it does not break them out. Give it a shot if you haven't, it's amazing.
Also, I have oily skin aswell, but this works really well.