1) Getting messed up = refers to becoming whatever the condition is (in a bad situation)
to get messed up or getting messed up=slang that means to be drunk, drugged or having some sort of problem about something.
- Getting messed up is something I try to avoid. [getting messed up=subject of the sentence. See being messed up below for more grammar.]
Here, the verb get means become. Become is quite formal and in everyday language get is often substituted for it:
- He got drunk last night. [rather than became drunk]
- He got rich last year playing poker. [rather than became]
Get rich, get drunk, get sick, get well [after being sick] are common examples of get + an adjective, to mean: to become rich etc.
2) Being messed up= refers to being in a state or condition
When we take the verb be and make it being + verb or noun, it refers to the subject of a sentence.
Being messed up is not fun. being messed up = the subject of the sentence and the state in which the person is in. It is called a gerund noun or gerund phrase. It can also be used as a complement.
He didn't like being messed up but he didn't know what to do about it.
Being poor is really a terrible thing.
[Note: careful with what adjectives you use with get (become). Not every one works.]