Teens with privacy end up staying in their parent's house until their mid to late 30's. There is a reason why kids have this strong need for privacy, it motivates them to get a job and move out - or to go to college or to join the military.... The less privacy they have as a teen, the more successful they are in later life.
As for masturbating: they way you have worded this and the way its been dribbled out through this thread it reminds me of a trolls way of getting attention. It feels trollish.
Let us assume for a moment that you really are not a troll and you have lead a remarkably sheltered life and that the internet is a new experience for you (plus you have no friends, no school mates, etc) .
IF you are getting too much friction on your penis from masturbating, then you are squeezing too hard. No hole that you will put your penis in in life will be as tight and as rough as the human hand. Loosen up your grip. No anus, no mouth, no vagina is that tight.
Secondly, there is no way you can thrust your hips as fast as you can 'beat off'. The human arm moves much faster than the human hips. No human will be able to sustain the fast repetitive neck movements that simulate how you move your hand in order to give you head that way.
Thus, with all of this masturbating you are desensitizing your penis and when the time comes when you eventually do have sex with a real person, you will find that they will have to work very hard, or you will have to work very hard in order to enjoy the experience to its fullest.
Suggestion: Masturbate less often, and do it slowly with a very, very loose grip.
Clean up: No do not use a sock or a t-shirt or any other article of clothing. Semen and sperm stain (yellow) materials. It is largely due to the high quantities of proteins, but other chemicals and organics in the mix also work to stain.
Get yourself a rag - say an old t-shirt that has been re-purposed, cut into swatches large enough to clean up, but small enough not to be worn as a shirt again.
Wash the rag often (like every time after you have done the deed). Wash it yourself, in the bathroom sink - shampoo and conditioner works well on natural fibers like cotton. Or throw it out.
Paper towels work as well.
As for the privacy issue, late, late nights may be your only alternative. OR go to bed early. If you commonly go to bed at 10 pm, go to bed at 9:30m. Really there is no need to masturbate at 1 pm in the afternoon or when ever everyone else is up.
Make your own privacy. Steal it from the wee hours of the morning.
Around here in my household, I get all the privacy I need at 5-8am in the morning. I go to bed early and wake up at the crack of dawn or earlier, come out into the living area, drink my coffee, surf the net, do handstands and If I was inclined I also have the time to masturbate or do other private things like pick my nose.