Getting plenty of rest will help to build your immune system to fight the sickness faster. Your body repairs and rejuvenates while you sleep.
Yes you can. You can get MUCH worse than it already is. 
The typical antonym for better, is worse. However it can also be - more ill, sicker, unhealthy, bad, detestable, disagreeable or unpleasant.
Sadly it is getting worse in the whole world.
its getting worse
deteriorating
worse.
Depends on what you define as gun violence and where you look. Subjectively: It is getting worse in UK, despite near-total gun ban. It is not getting worse in US.
worse
media
Getting worse.
no
Yes, illnesses become worse as time goes by.