Your English is pretty good. It is clear. You've written a long, complex sentence. It is grammatical. A native speaker would make different choices of words and word ordering. "Tickling" is not a good word choice. "Tickling" literally means this: https://www.youtube.com/watch?v=8W5In5gyiII "Tickling" feels good and bad at the same time. It means something that makes you laugh. "Nagging" or "bothering" would be better. With some other small corrections, you could say: "Here is a question which is nagging at me: at school, why were we told to write "have got" instead of "have" in sentences when, only now, I learn that writing "have got" is colloquial?" The answer to your question is: schools are like that!

The verb 'tickle' means 'chatouiller'. It's used the same way as in French in a physical sense: She tickled the baby's tummy to make him laugh. This angora pullover tickles a bit. In a more figurative sense, something that 'tickles' you is something that makes you laugh or amuses you. A question can't 'tickle' you, though - that's not how we use the word in English. The best way of saying this is 'a question which is bothering me'. NB Let us know if you want us to comment on what you've said about 'have' and 'have got'.

Thank you for your comments. I understand better now why it is good to learn "have got".

I use 'have got' a lot. But it's nearly always contracted to "I've got" so it's as quick to say as 'I have." I've got a cold/I have a cold. (I've a cold - I say this sometimes too.)

I have a couple of theories as to why you're taught "have got" in lessons: 1) the UK is a neighbouring country and this is a typical pattern in speech. You'll probably run into it in reality, so it makes sense to learn it in school. 2) Even though "have got" in the sense of possession is not present perfect, the pattern is similar. Therefore, if you're familiar with this structure, your first encounter with present perfect may be less of a shock because you're already familiar with "have" as an auxiliary verb (plus its contractions). ...any other thoughts on this? :)