I think what you're trying to say is something like
Perhaps there are many other expressions to say that in your mother tongue, but this is the only one that I can think of that gets my idea across correctly.
but that totally avoids the question in your title. Oops. So, let's ignore the sentence and just look at the two words in question.
One of the definitions of straight is, indeed,
right or correct, as reasoning, thinking, or a thinker.
(That's definition #8 out of 43 at Dictionary.com)
This is, at root, a metaphorical extension of the basic meaning of straight, namely, "not crooked". The opposite of this usage of straight is "confused".
Right, on the other hand, would generally have antonyms like "incorrect" or "wrong". The two words can be interchangeable:
I can never get it straight: do you feed a cold and starve a fever, or is it the other way around?
The above would mean pretty much the same thing if you substituted "right" for "straight". But in many cases, only one of the two words will work:
Before you can teach that concept to others, you have to get it straight in your own mind.
For the life of me, I can't learn the right way to fold up a map.
In both of these sentences, "right" and "straight" are being used in the sense of "correct", but you could not interchange them without either getting nonsense ("the straight way to fold up a map") or a subtly different meaning ("get it right in your own mind").