Is it possible for a person to have AIDS if they were cut by a razor and a small amount of blood came out, and tests did not show anything after a week, knowing that they suffer from obsessive-compulsive disorder?

The cure for obsessions (waswas) is to ignore them and not pay attention to them. Giving in to them leads to corruption in both religious and worldly matters. Therefore, one must not give them any importance. Remember that what was destined to befall you could not have missed you, and what missed you was not destined to befall you. Have a good opinion of Allah, rely on Him, and entrust your affairs to Him, for Allah decrees nothing for His believing servant except what is good for him.