心配かけてごめんねって英語でなんて言うの？

I'm sorry for worrying you. I'm okay now'

This is a kind way to apologize for any concern your illness may have caused. 'I'm okay now' reassures them that they do not need to be worried anymore and that you are feeling better.

"I caused you to"...is a handy little phrase...meaning: "it is my fault" "Its down to me"
"I made this happen"....IE the result of "Cause and effect".
We cannot help if our friends worry about us... however we can tell them we are sorry of we ...."Caused them to worry"

Native speakers will often say "I'm fine", even when unhappy or ill, to stop others from worrying. We also say it if we don't want to talk about our feelings or go into detail about our day. In general, we also say "I'm fine" as the standard response to the popular conversational greeting "How are you?".

By adding "please don't worry" at the end, you are giving reassurance to the person asking you that you really are feeling fine and that you are not just saying "I'm fine" to stop talking about your health and feelings.

Including "please" shows that you too care about the person asking the question and you appreciate that they want to know how you are.

formally you could say something like "sorry for concerning you"
otherwise you could say "I'm sorry for making you worry"

When someone tells us that they were worried while we were sick we mostly want to thank them for being worried. We would say something like 'Thanks for your concern" which is simple and polite. "Thanks for thinking about me" is basically the same thing but it goes a little deeper, saying that you acknowledge that they were thinking of you. "Sorry for putting you through that" goes a step further and says that you are sorry that they were worried.

This would be a good way of apologising for causing them concern over your illness and would also be reassuring them that you are ok now.

If you are not well you can say any of these phrases to indicate that you are ok and there is no need for them to worry. In England, particularly if you are a man, we have a phrase for this called: "man flu". If you say, "Don't worry, its just man flu!" This indicate that it is a very minor sickness / cold and there is absolutely no need to worry! In England, it is a kind of joke so its nice to say this.

"Thanks for your concern"
Is a polite phrase that implies that you are thankful for someone being worried/concerned about you, this may of been because you were sick.
"Sorry to make you worry about me"
This suggests that they were worried about yourself from, example, being sick. and you are apologizing for making them worried/concerned/scared.