Today since I woke up I been having lots and lots of erections all day, even when I don't want an erection. Is this normal? And I get this warm sensation in my penis as well while I am having an erection. I feel as if something wants to come out, but it doesn't come out, at that same time. Is all this normal?
Yes, it is all normal. Your body has various ways to bring its needs to your awareness. When the percentage of water in your blood drops to a certain level, you begin to feel thirsty. When your upper colon becomes empty, you begin to feel hungry. Hunger and thirst are desires produced by your body that makes you aware of the fact that you need to eat and drink.
Now that your body has gained the ability to produce semen, a new desire is now present, a desire for sexual release. Right now, because it is all brand new, your body is over reacting to the signals. What signals? Your seminal vesicles, which produce your semen are getting full. Your body knows you need another ejaculation to release the excess, so you get hyper-sensitive to anything remotely related to sex and to many things that have absolutely nothing to do with sex.
As a result, your brain is acting like a driver with a lead foot, pushing the arousal button and causing you to have erection after erection. Your reaction to it ("Not NOW!") is the beginning of the training your brain needs to go through to know when to trigger erections. The warm feeling in your penis and the feeling that you need for something to come out is your body wanting to move semen into the ejaculatory duct. You're feeling the switching mechanism in your prostate move from "normal" mode where you can urinate to "sex" mode where you can ejaculate.
All that is missing is the extra stimulation needed to cause the seminal vesicles to squeeze semen into the ejaculatory duct and for you to have an orgasm to trigger the ejaculation. If nothing else happens, then very likely you will have a wet dream that night as your body takes care of its need on its own.