How can I perform my Dhuhr and Asr prayers at home after returning from work at the hospital, knowing that there are those who tell me the prayer time has passed?

The fundamental principle is the obligation to perform each prayer within its prescribed time. Combining two prayers is impermissible except due to a valid excuse. Deliberately delaying a prayer beyond its time without an excuse is among the major sins.

You must pray before the time expires, even if at your workplace. If you are unable to pray at the appointed time because of harm that would befall what you are hired to guard or repair, or if there is fear of harm afflicting patients, then you are permitted to combine the two prayers by delaying the first (jama‘ ta'khir), with the intention of doing so at the time of the first prayer. Many scholars have permitted combining prayers out of necessity.