Are my prayers valid after discovering the paint line on the nail, and must I make up the prayers prior to its discovery, and if so, should I make them up shortened or in full, knowing that I was traveling?

The most effective cure for waswasah (whispers/obsessive thoughts) is to ignore it and pay no attention to it. Some scholars have been lenient regarding minor impediments that do not cause harm. This was the choice of Shaykh al-Islam Ibn Taymiyyah, such as slight dirt under the fingernails and similar matters. This also includes cracks that appear on some limbs. Indeed, hardship brings ease, and the more a matter narrows, the more it expands. Therefore, all your prayers performed before washing a location with a minor impediment are valid, and you are not required to repeat them.