All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Our answer to you will be in the following two points: firstly: should one perform istinjaa' immediately? Secondly, is it enough to perform istijmaar (purifying oneself from defecating or urinating) with a tissue and the like if the impurity spreads beyond its usual place?
With regard to the first issue, a group of scholars stated that it is not an obligation to purify oneself from impurity before wanting to perform the prayer, and they did not make a difference between when the impurity is in its usual place and when it goes beyond its usual place. Imaam an-Nawawi said in Al-Majmoo’, “It is not an obligation to perform istinjaa' immediately but it is permissible to delay it until one wants to purity himself or wants to perform the prayer...”
Ibn Muflih, from the Hanbali School, said in al-Furoo’, “Ibn al-Jawzi said, 'It is not obligatory to purify oneself from defecating or urinating, or from being in a state of impurity, before wanting to perform the prayer; rather, this is only desirable…'”
The Fiqh Encyclopedia reads:
“The obligation of performing istinjaa' is for the validity of the prayer; it is for this reason that Ash-Shabraamallisi from the Shaafi'i School of jurisprudence said, 'It is not an obligation to perform istinjaa' immediately, but only when one actually wants to perform the prayer, or when the time of the prayer starts and he does not want to perform it at its beginning time. When the time of the prayer starts, it becomes an extended obligation according to the extent of available time (for the prayer), and a restricted obligation when the time (of the prayer) is short.' Then he said, 'Yes, if he relieves himself during the time (of the prayer), and he knows that he would not find water in time, then it becomes an obligation to use stone immediately'...”
Some scholars hold the view that it is an obligation to perform istinjaa' immediately, based on the Hadeeth in which the Prophet passed by a person in a grave and said, “He is being tortured not due to a major sin but due to him not cleaning himself after urinating.” [Al-Bukhari and Muslim]
Ibn Hajar said in al-Fat-h, “It is a warning against being stained with urine (and not cleaning it with water), and this also applies to other impurities in one’s body or clothes. This Hadeeth is also evidence that it is an obligation to remove impurities immediately, contrary to those who restricted the obligation to only when the person is willing to perform the prayer.”
The second issue is that if the impurity spreads beyond its usual place, then it is not sufficient to make istijmaar with a tissue and the like; rather, it is a must to make istinjaa' with water according to many scholars. The jurists of the Hanbali School stipulated that if the discharge goes beyond its usual place, then it is an obligation to use water in those places to which the discharge spread, and it is not sufficient to perform istijmaar for it because istijmaar is a concession and it is limited to the usual place and should not exceed this extent because this is contrary to the principle. However, Shaykh Ibn Taymiyyah from the Hanbali School of jurisprudence, holds the view that if the discharge goes beyond the usual place, it is still sufficient to perform istijmaar for it, as there was no estimation about this from the Prophet . Ar-Rawdh commentary reads, “If the discharge does not exceed the usual place, like when it spreads on the glans and extends further in an unusual manner, then it is only water that should be acceptable in washing those places that are beyond the usual place, because in principle it is an obligation to remove impurity with water. Istijmaar is only given as a concession because of the repeated spread of impurity in the usual place, so if the discharge goes beyond its usual place, then the concession does not apply to it”. The Shaykh (Ibn Taymiyyah) determined it by, “If the feces spread to half the bottom of the buttocks or more, and urine spreads to half of the glans and more, then in this case using water is a must.” This is explicitly mentioned by Ibn 'Aqeel and others. However, Al-Ikhtiyaaraat (of Ibn Taymiyyah) reads, “It is sufficient to perform istijmaar even though the discharge exceeds the buttocks for the general evidence, and it was not reported that the Prophet determined the extent of this.”
If the impurity stains the clothes and a person wants to pray, then it is enough for him to cleanse the place where there is impurity, so he washes it, and he is not obliged to change his clothes.
Finally, you should avoid waswaas (obsessive whispers) as your question implies that you have some whispers in this regard. May Allaah safeguard you from them.
Allaah knows best.