What are the rules for looking for a new job while you still have one?
Get up one hour ahead than usual and spend that hour on searching. Also during lunch breaks, leave the building where you are in to log into your personal lap top to do the search. After work, spend an hour at a Starbucks or library to do the same. You should also plan to reserve some time during the weekend for searching. I recommend to use special websites which display all vacancies in one place, like https://in.jobsora.com/
Attend interviews after hours (most prospective employers will understand that) or take a personal or vacation day if you have more than one interview to attend. Good luck.
Companies understand that you cannot jeopardize your current job while seeking a new one. They will often try to schedule interviews very early in the morning or very late in the afternoon to give you as few hours away from your work as possible. Claiming you are sick is lying. Claiming you have personal business is true and they do not have to know what the personal business is. I do not think it is a good idea to tell your current employer that you are job hunting. They may be looking to downsize and choose you.