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tonyck 2 posted:However, can "have" be used as a dynamic verb in the following sentence?
Don't come close to me. I am having a bad cold.
No, that sentence doesn't work. "Have" can't be used in the progressive in that context. When you talk about "have" as a dynamic verb, you are probably thinking of uses like "We are having lunch" or "She is having a baby," where "have" refers to eating and giving birth to, respectively, not to owning or possessing. When one has a cold, however, one has it in a stative sense (one "possesses" a cold), and the fact that colds are temporary doesn't make it OK to use the present progressive. But you can say:
(a) I am suffering from a cold.
(b) I am recovering from a cold.
(c) I am fighting off a cold.
(d) I am feeling under the weather.
There are some contexts in which "have" is stative and works with the progressive. I am thinking of constructions like "I am having a hard time believing that" and "He is having some trouble." While those are interesting exceptions, the important point here the present progressive does not work with "have a cold." Now, the past progressive, the past perfect progressive, and present perfect progressive with "have a cold" are possible when there is a frequency reading, i.e., when you are talking about more than one cold:
(e) I have been having a lot of colds.
(f) I was having colds regularly.