It's funny how the same questions come up over and over again here. Wouldn't it be great if Italki had a good way to browse old answers to questions that everybody has? Anyway, here is a similar question and some responses from yesterday: https://www.italki.com/question/347185. But if you just want a quick answer to what you would use yourself, I would stick to "have" rather than "have got". It always works, in both US and UK English, and in any register and tense.

Эти фразы могут быть взаимозаменяемы без изменения смысловой нагрузки, можно сказать как "I have a cat", так и "I have got a cat", в значении обладания чем-то. В Британии чаще используют have got, в Америке i have. Have got принято так же считать неформальным стилем. Есть устойчивые фразы которые употребляются только с have, такие как: have breakfast, have tea, have a bath.. etc в таких случаях разница в употреблении этих конструкций есть. Для сравнения: Have a bath- принимать душ НО Have got a bath- иметь в квартире/доме душ/ванну. или "I have sandwich for lunch- На обед я ем бутерброд" НО "I have got some sandwiches. Would you like one?- У меня есть пару бутербродов. Хочешь?" Have got имеет форму только Present Simple и никогда не употребляется в других временах.

I was wondering about that the other day....didn't really reach a conclusion! Some say "I have" is slightly more formal than "I have got," even when the latter is not contracted into "I've got." maybe that was true years ago but I'm not sure about today. It seems the difference between them gets smaller and smaller. have you ever been told you can't use one in place of the other? I can't think of such a case. It's probably just my imagination, but it feels like "I have" is used more often for something that you had no control over-- that you didn't deliberately plan on getting, like a disease, racial features or a family member. "I have got," however, sounds like you're talking about something you have gone and and acquired deliberately, like pets, cars, furniture. Could very well be wrong, though.

In US English, "I have" is generally preferred. "I have a headache. I have a husband. I have a briefcase with 10-million dollars stashed in the trunk (boot) of my car." "I have got" is generally considered a "lower class\less educated" use of "I have." It can be used for emphasis, though, and be completely acceptable, as in "I have got *such* a bad headache!" "I have *got* to get some sleep." 'I have *got* to get to the bathroom!" "I have *got* to get that assignment finished."