Here's some help with talking about getting sick and catching a cold: "Sick" is an adjective, and we usually use "sick" with the "be" verb:
- I am sick. (Not "I have sick.")
- Jack is sick today, so he is not coming to work.
- I was sick last week, but I am feeling better now.
Note that you can also say “I got sick,” “I became sick,” “I feel sick”, but not “I have sick.”
"Cold" is an adjective,