Is the new job lawful or unlawful, considering that the transition to it involved concealing some details from the previous employer?

It is not permissible for you to seek permission to leave work under the pretext of going to the doctor when you intend to go elsewhere, because the permission is restricted to a specific time estimated for going to the doctor and returning. Furthermore, if a medical certificate is issued for someone who is not ill, it is considered a false testimony. You could have sought permission with a genuine excuse or taken a leave. A Muslim does not lie and does not obtain an un உண்மையான medical certificate. He should be content with what Allah has destined for him, for "the Holy Spirit breathed into my soul that no soul shall die until it completes its term and consumes its provision. So, fear Allah and be moderate in seeking, and let not any of you be carried away by the delay in provision to seek it through disobedience to Allah, for verily, what is with Allah cannot be attained except through His obedience." You must seek forgiveness and compensate your workplace for that day or ask for their forgiveness.