Learn English – I’m living in a sharing apartment

• 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

How do we say naturally that we want to keep in touch continuously.

It would be okay to leave just one expression:

1. Please keep in touch with us after you get to the college.

You might add some adjunct to it to stress your need for a continuous contact:

2. After you arrive at the college, please keep in touch with us at all times.

.. sentences 1 and 2 would mean that the period of "continuous contact" will start at the moment of arrival to the college.

You can say:

3. Please continue keeping in touch with us when you arrive at the college.

.. this would mean that there is an ongoing contact between the parents and the son, and that the parents want to remain in the same kind of contact with their son after he arrives at the college.

You indeed can combine "keep on" + "keep in touch", but you would need to turn the second expression into "keeping in touch":

4. After you arrive at the college, please keep on keeping in touch with us.

.. the meaning would be similar to sentence 3.

But people tend to avoid having two similar expressions close to each other, because such constructions look strange, despite being grammatically correct.

You can use "keep on keeping in touch" as a kind of wordplay to amuse yourself or your listeners, to make someone stop and notice this strange combination, but not too often. (0:

There is an expression that uses this effect: "keep on keeping on" - meaning "keep trying, keep doing what you are doing". It's used in poetry and songs:

And when finally the bottom fell out
I became withdrawn
The only thing I knew how to do
Was to keep on keeping on like a bird that flew
Tangled up in blue