I had a gum cleaning and the gum became swollen with pus. Did the bacteria get pushed in?

It is difficult to comment on the specifics for you or give you a diagnosis from this information alone.

But regardless of the treatment, If a gum pocket is inflamed and you have periodontal disease, your gum pockets can be ulcerated at the pocket base. That means there is a break in the lining.

Depending on the exact community of bacteria and your immune defences, inflammation can become infection sometimes (this is a Periodontal or Peri-apical Abscess).

It is possible this can happen with whatever is put into a gum pocket (including oral hygiene aids which you use at home), as disrupting the plaque bacteria can mean it becomes trapped rather than flushed out.

We recommend you seek the dental advice to minimise your chance of things deteriorating and causing more trouble. Hope things settle for you soon!