Is the prayer valid if the worshiper forgets the number of prostrations, then adds another prostration based on the action of the person next to him?

What you did is correct, provided you are not prone to obsessive doubts (waswas). In your case, the prostration of forgetfulness (sujud al-sahw) should be performed after the salutation (taslim). If someone doubts in their prayer whether they performed one prostration or two, and they are not frequently afflicted by such doubts, then they should build upon the lesser number (assume one) and perform the second prostration. Then, they should perform the two prostrations of forgetfulness after the salutation. As for someone who experiences frequent doubts, they should disregard the doubt.