wahoo: let me try to re-iterate the relevant facts I sifted from your text:
- you have worked in an employment in Germany with a fixed salary, public
health insurance (AOK)and all for a couple of month
- the time you have been employed was not long enough to make you eligible for unemployment beenfits
- you are now looking for to get a residence permit/visa as a self-employed for which you need to show proof of health insurance
If these facts are correctly summoned up from your info, the following would be your situation. If some of the facts are not correct, pls specify/clarify so that the right answer can be given to you.
1. since you already have a membership from your past employment in a public health insurance, you continue to be a member regardless of your employment/income situation. However you must inform the AOK about your change of employment status and income and give them a bank information from where to draw the monthly premium if, what I assume, the premium was paid from deductions of your pay-check by the employer.
Of course you will be a bit shocked when you see the total you will be charged now by the AOK since now you have to pay the full premium whereas in the past your employer picked up half of the costs. Which is exactly the case you need to inform AOK about your current no-income-situation in order to get the lowest possible premium computation awarded (based on an income as self-employed of roughly 1.200.- EUR/month minimum). If you don't get in contact with AOK and if the don't get a premium for your health insurance for three month they'll kick you out and you would have a hard time of getting re-accepted voluntarily again later.
2. depending on your chances to get back into employment or to continue a career as freelancer/selfemployed you have of course also the options to take on private health insurance from German or international insurance companies. if you are young, single and healthy this would definetly save you some costs right now. If you'd take a private German health insurance you would also have the security that this insurance stops to be effective (and to cost money) whenever you pick up a new employment with compulsory public health insurance, thus you'd avoid the danger of being liable to pay for private health insurance AND public health insurance parallel for some time which would be the case with most international health insurance being based on yearly contracts.
If you want to see the difference between lowest possible public insurance costs for you and similar coverage by private
health insurances, contact an independent insurance broker to work this out for you. But make also sure that you discuss all consequences of going the private way with him in detail before you opt out from public system you are already in. There are pros and cons and one size does definetly not fit all...
Cheerio