I had to clean out a freezer with 1 year old rotting meat. Could I get sick from breathing around it?

Rotting meat. Rotting meat will only make one ill if one ingests meat that is infected with a bacteria or touches its bacteria filled juices & then touches mouth/mucous membranes or touches contaminated surfaces and then touches one's mouth or mucous membranes.
Could ya?- yes. Aitborne pathogens, mold spores could become a problem.