The word "sick" means "ill", "poorly", "unwell", etc. However some youths have started to use it to mean something else, such as "amazing" or "awesome", but this usage will probably disappear as quickly as it came about, in much the same was as "rad" and "groovy" are now both virtually extinct. If you're over about 20, using "sick" in this way is not advisable.

When referring to "sick" as an illness, ailment, or disease, it is considered bad, and usually only refers to a person or living being. Usually, when "sick" is used as slang, it is considered awesome and refers to an action or inanimate object.

You should be able to tell by context, but you might be able to guess by the age of the speaker. My high school students sometimes refer to something as being "sick" when they think it is awesome. However, I have never heard anyone over 30 use it that way. Sick is also slang, so if it were to be used in any sort of formal or written communication, it would likely be the traditional meaning (in poor health). Hope this helps!

恶心

You can usually tell by the inflection on someone's voice when speaking, but in writing, people will usually mention an ailment (disease, illness, etc.), but in a good context, it usually means awesome.