Answered by Shaykh Yusuf Weltch
If water splashes on the arm while washing hands (assuming hands were naajis), do I need to wash the arm too?
If remnants of soap are left behind on the hand after washing them (assuming hands were naajis before), is this clean or not?
In the Name of Allah, the Most Merciful and Compassionate.
You don’t need to wash your arm since there is no proof that the splashed water became impure from the hand. [Shurunbulali, Maraqi al-Falah]
Rulings of Purification Not Based on Conjecture
If you are unsure if there is impurity present or that impurity has transferred, ignore it and never second guess. Even if, hypothetically speaking, impurity was present, the prayer is still valid with a small amount of impurity. [Shurunbulali, Maraqi al-Falah]
You should abandon all conjectures, misgivings, and/or second thoughts, even if that means praying with impurity on you, then allow any manipulation by the Shaytan.
Allah Wants Ease For Us-Shaytan Wants to Make Religion Hard
Allah Most High says, “Allah wants for you ease and does not want for you hardship.” [Quran, 2:185]
He also says, “…and He (Allah) has not placed upon you in the religion any undue hardship.” [Quran, 22:78]
Kindly check this as well:
A Reader on OCD and Waswasa (Baseless Misgivings)
Hope this helps
And Allah knows best
[Shaykh] Yusuf Weltch
Checked and Approved by Shaykh Faraz Rabbani