he could have caught cold and gotten sick??
he could have caught cold and gotten sick
he could have caught cold and got sic

which of these is correct?

Question

he could have caught cold and gotten sick??
he could have caught cold and gotten sick
he could have caught cold and got sic

which of these is correct?

Answer

E.T, 

"to get sick" is an American expression. The past participle "gotten" is not used in British English. 

In your examples, #1 is correct. The tenses need to match. 
He could HAVE CAUGHT cold and he COULD HAVE GOTTEN sick. 

I get sick. I am getting sick...... present 
I got sick..... past simple 
I have gotten sick...... present perfect 
had gotten sick....... past perfect


Of course, if you speak British English you will prefer to use the past participle "got", instead of gotten.

Answer

He could have caught a cold and got sick.

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