What is the ruling on my ablution and prayer if I performed ablution and prayed, then found something under my nails and doubted whether it was there before or after ablution, with uncertainty about it being a part of the skin, and does Sheikh Ibn Uthaymeen's saying, "One should not pay attention to doubt, whether strong or weak, unless certainty is attained," apply to my situation?

Scholars have differed regarding the ruling on minor dirt under the fingernail that prevents water from reaching the skin, whether it invalidates ablution or not. Al-Nawawi held that if it prevents water from reaching, ablution is invalid. Whereas Al-Ghazali considered it excusable due to necessity. The Hanbali school of thought holds that minor dirt under the fingernail does not harm, and purification is valid with it. If you doubt whether it is an obstruction or a piece of skin, the default is the absence of an obstruction, and purification and prayer are valid. Certainty is not removed by doubt.