A widow is supposed to observe a mourning period of four (4) months and ten days. This is mandated by the order of Allah in the Qur’an, “Widows shall wait, keeping themselves apart (before they remarry) for a period of four months and ten days, after their husbands’ death. When they have completed this set time, you will not be blamed for anything they may reasonably choose to do with themselves. Allah is fully aware of what you do.” (Al-Baqarah 2: 234).
During this period she should reside in the marital house unless she is in need to go out for a legitimate reason. Going to consult a doctor is one of these reasons.
It is noteworthy that if the doctor is a male she has to observe the general Islamic rulings concerning women being treated by male doctors.
Watching tv does not itself violate the sanctity of the morning period, but it is the content she watches that may do. So, if she is watching news or any other serious content, this is permissible. Needless to say that there are some generally prohibited contents that must be avoided any way.