Take a look at the original sentence again:
Several students sat sneezing and sniffling in their
seats, Jason always wore too much cologne,
and allergic reactions kicked into high gear as the odor wafted through
the classroom.
You chose to fix it the correct way:
Several students sat sneezing and sniffling in their
seats. Jason always wore too much cologne,
and allergic reactions kicked into high gear as the odor wafted through
the classroom.
Several students sat sneezing and sniffling in their seats is a main clause. Jason always wore too much cologne is the second main clause. You are always correct when you use a period between the two main clauses that create the comma splice.