Halachic and rabbinical law on spiritual contamination caused by a seminal discharge. Reference is to Leviticus 15
This article cite several sources that explain that you do not have to wait seven days, as you write, but they stress some important rules. One of the rules is that the semen should be washed away.
The Alter Rebbe in his Shulchan Aruch HaRav explains when and when one does to have the "feces" - e.g. semen to be washed away:
Even with regard to semen on the skin, it is advisable to follow the stringent view as with feces notwithstanding the fact that [the semen] is covered by clothes,22 even though according to the letter of the law it is not comparable to feces at all. Nevertheless, it is not necessary to wash with water unless it is already dry. If, however, it is still moist, it is sufficient to remove it with a cloth.
When does the above apply? To [semen] on one’s skin. If, however, it is on one’s clothes and is covered, [reciting the Shema] is permitted even with regard to feces, as explained above.23 Certainly this applies with regard to semen, for it is not comparable to feces at all according to the letter of the law. Nevertheless, certain of the pious men of the early generations would engage in intimacy naked24 so that semen would not attach to their clothes even though it would be covered from above. Similarly, they would be vigilant that their clothes would not [be soiled by] even a drop of urine, and certainly not by a drop of feces.
The article also quotes the Ateres Zekeinim (siman 40:3), where, in regard to tefillin, it is written that one could wear tefillin, "even though he is considered impure"
1: See Admur 76:4 regarding Davening that a) It is proper to be stringent by semen just as by feces, and hence one is not to Daven if the semen is on his skin, until it is washed off, even if it is covered by clothing. 2) If it is not on the skin but on one’s clothing, then if it is on one of the inner clothing that is covered by exterior clothing, then it does not prohibit Davening. However, if it is on the outer clothing, then it must be cleaned/washed off. 3) Some Chassidim were stringent not to have semen even on their inner clothing.
2: Poskim ibid; Ateres Zekeinim 40:3 “He may wear them even though he is considered impure”