As-Salamu `Alaykum. First excuse my english please. My question is about purity. I was impure in my private parts due to urinary incontinence, but also have some cracked skin in that body area. Now I'm afraid I defiled all the house by walking, with the pieces of (probably) dirty skin. What should I do? I'm victim of OCD by the way. Jazakum Allahu Khayran.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

You should overlook these whispers (obsessions), ignore them, and not pay any attention to them. There is no part of the house nor anything else that is impure; on the contrary, everything that you deal with is pure as long as there is no trace of impurity on it. The mere assumption and suspicion that it is stained by impurity shall not be taken into consideration.
If you suffer from incontinence, as you mentioned, then that impurity that exits on your private parts because of the cracks is excused according to the Maaliki School of jurisprudence. There is nothing wrong with you following that opinion to avoid hardship and mitigate difficulties.

We ask Allah to grant you wellness.

Allah Knows best.