Is it a correct sentence?

Yes, but without the full context it is not possible to tell whether "the things" is the correct phrase. If you mean "things in general", delete "the". Given the second sentence, consider whether to say "are really high" rather than "have been really high".

What about this one,
the prices of things have been really for three days.

Anonymousthe prices of things have been really for three days.

You missed out something. Perhaps you meant this:

The prices of things have been really high for three days.

One more question, Sir. You mean 'are really high' and 'have been really high' are almost interchangeable even though 'have been really high' is better?

"have been really high" is talking about the situation in the recent past, leading up to the present. Often it may include the present. However, if there is a contrastive context (e.g. you go on to say something like "... but now they are lower again") then it may exclude the present.

"are really high" is talking about the situation now. "We can't buy anything with ten dollars" is also ta

could you please check one more sentence here,

The prices of things have grown up, we can't buy anything with ten dollars. I am sure this is correct, isn't this?

AnonymousThe prices of things have grown up, we can't buy anything with ten dollars. I am sure this is correct, isn't this?

"grown up" is not right. My guess is that you are thinking of "gone up". Also, your sentence is a comma splice (two independent clauses incorrectly joined by a comma). This is one way to fix it:

The prices of things have go