This one with since is fine.

The situation has become worse since [the last accident/that meeting/the breakdown].

But if we use after, can it still be grammatical? if so, is it okay, awkward, etc.

The situation has become worse after [the last accident/that meeting].

By the way, does the sentence below sound natural (in whatever common contexts such as personal health or fixing a vehicle)?

The situation has gotten worse since [the last accident/that meeting].

In any case, if you cannot decide but you know of a specific scenario where any of the above could be used, then please write away.