There's some idiomatic confusion here with the word for, a preposition that has been with English since its beginnings and which therefore has had centuries to develop different meanings in varying contexts. The original OED took almost four pages to outline 11 major classifications with 31 separate major meanings for the preposition. There are two meanings at play here, the first is to the advantage or disadvantage of [someone]; the second, on behalf, in place of, on the account of [someone]. Occasions for ambiguity arise. Thus
At the meeting, she spoke for me
can mean either she spoke in my favor, to may advantage (perhaps I was a candidate for office) or she spoke in my place, on my behalf (perhaps I was unable to go and speak for myself).
don't make trouble for me
is generally understood to take the first meaning mentioned above, in other words, don't place trouble upon me. That's not what your friend meant, of course. She meant the second meaning, that is, don't trouble yourself on my account. This is better phrased as
don't trouble yourself for me
don't take trouble for me
which is a trifle stilted and dated.
In any case, you should bring your gift anyway and say to your friend
It's no trouble for me; I like getting gifts for you.