Is ablution considered valid if there was a small cut bleeding during ablution, and I found a tiny drop of blood on my finger after finishing it, knowing that I suffer from obsessive-compulsive disorder?

We advise you to shun intrusive thoughts (waswas) and strive to rid yourself of them. Your ablution is valid, because the default state is that water does not change due to impurity; it remains pure. So, if you doubt the contamination of water that is certainly pure, it is permissible to purify yourself with it, because the side of purity is more probable and is supported by certainty. As long as you are not certain that the water has changed due to impurity, the default is its purity, and therefore, your purification is valid.