Answer:
A and C are correct.
B is the run-on.
Explanation:
There are several ways to correct the error.
Add a period.
I am allergic to fur. I adopted a turtle instead.
Add a semi-colon.
I am allergic to fur; I adopted a turtle instead.
Add a coordinating conjunction.
I am allergic to fur, so I adopted a turtle instead.
Add a subordinating conjunction.
Because I am allergic to fur, I adopted a turtle instead.
Add a conjunctive adverb.
I am allergic to fur; therefore, I adopted a turtle instead.