You are really close, so lets try to break it down for you.
Here's your sentence:
I'm going to break it down from left to right.
このままだと: このまま translates to
in this state, so good job on the translation here. だ is the plain form です、so you're correct here. The と、however, is where our translations will differ. This と is actually translated to
if, (see this link) so this phrase translates to something to the effect of
if this is the current state.
自分だけじゃなくて: The main grammar here is found at the end,
じゃなくて. You're right to say that this is a conjugation of じゃない. When ending a verb (to be in this case) with a 〜て, you give the impression that there is more to the sentence. For sake of simplicity, lets just describe this as an compound particle (and/but in particular). Really, you're creating a compound sentence. (see this link) This phrase will be something to the effect of
not just me, but
世界も壊れるだろう: (notice the addition of も) This is as you translated, so I won't beat a dead horse.
The whole would would break also. The also in this sentence comes from も。
So, lets translate the sentence as a whole.
If this is the current state, not just me, but the whole world will break also.
(I realize @Naruto already posted a great answer, but I figured I'd finish my answer anyway since I was already really close.)