Q:

I am cold vs I feel cold vs I got cold

There are three sentences which makes me confused.
I think one of them is used to say you don't feel good or you literally are sick.
Other one is used to imply that the temperature in the room where you stay is probably lower than average so you are shivering.But you are not ill, if you turn the heater up, you will feel perfectly ok.
But which is one which or are they interchangeable so we need extra explanation what we want to imply?

I am cold
I feel cold
I got cold

And are there other phrases that can be used for these situations that we can be more clear on what we want to imply?
For example I heard

I am chilly

But I am not sure in which mean can it be used?

A:

I am cold: My temperature is low 
I have a cold: I am sick 
I've got a cold: I am sick 
I got a cold:    I became sick 
I got cold: My temperature became low
I had gotten cold: My temperature had become low

Whenever versions of the verb "to be" such as "is" or "am" is used, then it implies that the person's temperature is in question. If the verb "to have" is used, then it implies that the person has some affliction, disease or some condition. The exception is "I got cold" because "got" in this context means "became". The lack of "a" before cold shows that it is an adjective, and not a noun, however.
So "I am chilly" would mean that the person's temperature is low. If the person said "I have a chilly" then they would have a chili pepper in all likelihood

