English speakers like using "get" instead of some verbs like "take, be, become" etc.

'got' is the past of 'get' so I got sick means 'I was sick' or I became sick/ started feeling sick (past simple). Usually this tense is connected to a finished past time whether actually stated or implied. So normally you would say 'I got sick last week/ yesterday/ while I was at school etc 'To get' in this sense means to become or start to be, so the fact of being okay now is not implied unless you say it. If you got sick while you were at school and now you are home you may still be sick.

'got' is the past of 'get' so I got sick means 'I was sick' or I became sick/ started feeling sick (past simple). Usually this tense is connected to with a finished past time whether actually stated or implied. So normally you would say 'I got sick last week/ yesterday/ while I was at school etc 'To get' in this sense means to become or start to be, so the fact of being okay now is not implied unless you say it. If you got sick while you were at school and now you are home you may still be sick.