Yes. It is confusing. Here's the general rule: "Get and go are both used to mean ‘become’, but they combine with different adjectives. We often use get with words like dark, light and late; we use go with colours and words with negative associations such as mad, bald, bad: It’s getting dark now so be careful. Not: … going dark … He’s only 30 and he’s going bald. Not: … and he’s getting bald. We left the milk in the sun too long and it’s gone bad. Not: … and it’s got bad. However, with some adjectives such as old, sick, tired and ill, we use get: He got very tired walking to the match in such a large crowd. Not: He went very tired walking" https://dictionary.cambridge.org/grammar/british-grammar/get-or-go BUT note that the word 'mad' in the above paragraph means 'crazy', not 'angry'. I note that you said that you think it's okay to say "get angry."...it's not...you must say "get angry" (or "become angry"). It's unreasonable to assume that things like "angry" and "annoyed" are negative associations...I mean they are negative, aren't they? However, we do use get/become with these words. Also with adjectives like 'happy' & 'sad'. I think we might be able to propose a 'rule of thumb'..."We use get/become with adjectives that describe temporary emotional states."...I'm now waiting for all the examples of exceptions to this rule :-)

“Go annoyed” is nothing, “become and get annoyed” are the same and “get annoyed” is the most common.

"I am becoming annoyed." This means that something is in the process of annoying you. "Go annoyed", is not proper English. "Got annoyed" (Get annoyed is improper) is when something annoyed/bothered you already.

Both 'get'and 'become' are perfectly okay to use with 'annoyed'. 'go annoyed' is wrong...or at least non standard. I have never heard it before 'get' has a number of different meanings. One of those meanings is a synonym for 'become' . The past tense of 'get' is 'got'. Here's the description from a dictionary: "Get: reach or cause to reach a specified state or condition. "he'd got thinner" Similar: become, grow, turn, come to be used with past participle to form the passive mood. "the cat got drowned"

I've never heard anyone say "go annoyed." The other two are interchangeable.