The first sentence is grammatically wrong. “Before” in that sentence is acting as a conjunction and introduces a subordinate clause concerning temporal order. Such a clause requires at least a subject and a verb. When used as part of a verb, participles must be used with an auxiliary verb. Present participles such as “getting” form verbs in conjunction with some form of the verb “be” to indicate progressive aspect, which does not fit the situation.
The third sentence is the grammatically correct way to express the thought probably intended in the first sentence. Notice that “got” is used in this sentence as the simple past of “get” rather than the past participle.
You are correct that the second sentence, which is also grammatically correct, has a slightly different meaning. Here, there is no necessary implication that the situation got worse after the speaker left. What is implied is that the speaker was potentially a cause of the bad situation and left in order to prevent the situation from getting worse or that the speaker feared it might get worse. The implication is not that the situation did get worse after the speaker left, a matter of sequence, but that the situation did not get worse at least while the speaker was present. The difference in meaning is small and subtle.
What makes this set of sentences particularly confusing is that the preposition “without” introduces a phrase rather than a clause, and phrases do not contain a verb. So, the participle “getting” modifies “situation” and no auxiliary verb is required because no verb is needed. So, there is purely technical difference in the grammar of the second and third sentences that is not fundamentally relevant to the difference in meaning.
You have stumbled on to a set of sentences involving the varied uses of participles, the different aspects implied by present and past participles, the differences between clauses and phrases, and the fact that some words such as “before” sometimes act as a conjunction introducing a phrase and sometimes act as a preposition introducing a phrase. All of these are convoluted features of English grammar.
In short, sentences two and three are grammatically correct, but do mean somewhat different things.