Review the original item:
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 wanted to fix it this 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.
To delete the comma between seats and Jason would cause an equally bad problem, a fused sentence. A fused sentence occurs when you have two main clauses joined with no punctuation whatsoever. Several students sat sneezing and sniffling in their seats is the first main clause. Jason always wore too much cologne is the second main clause.
The spot between seats and Jason needs a stronger break than blank space.
You might want to consult the rules for fixing comma splices and fused sentences.