I read this passage recently - particularly verses 33-39 - and is struck me as a very odd passage. It is talking all about "The Oracle of the Lord" (in the version I was reading), and it reads very oddly.
The translation of the core word "Oracle" is massa, which can also translate as "Burden", which can help to understand the meaning - it is talking about not burdening people with messages supposedly from God. But it can be read quite differently.
One way of reading it would be to say "stop telling me that you have heard this word or message from God, because you are making it up". It is an interesting critique, I think, of some of the churches I have known that their use of something as being "from the Lord" puts it beyond reproach, and yet here is Jeremiah saying "I don't care if you credit it to God, shut up!"
Another way of interpreting the passage is to take the phrase as referring to burdens purely. It can be read as saying "stop burdening other people with the burdens you have taken on. Deal with them yourself, whether they are from God or not". How often have we heard that someone has a "burden from the Lord" for this or that, and so we should all feel similarly burdened and support. But this passage is saying "stop calling it a burden from the Lord - it is all yours. Deal with it, and shut up." I think that has something vital to say to us all, that those things that we have a heart for, that we feel are important to pray for or do for, are ours. They are not things that we should encourage others to be similarly burdened. Just because you feel that God had given you something to do - a burden in the positive sense - doesn't give you the right to burden - in the negative sense - others with it.
However, I do think there is something of both in the passage. The Old Testament (and occasionally New Testament) writers are never shy of puns or double meanings in their writings. I suspect Jeremiah meant both of the above interpretations, as well as the one that I suspect he intended most especially - the message that you should not burden other people with messages that you claim are from God. Which is rather a peculiar word from a prophet (especially one like Jeremiah, who most definitely did burden others with words he claimed were from God).
Of course, we do not know the precise situation and events that prompted this particular passage. It might have been that, as throughout Jeremiahs time, people were using what they claimed to be "Oracles from God" to pressure people into their own point of view - something we still see today. It might have been that people were taking the phrase "An Oracle from God" lightly, mocking his own messages by using it to justify anything they wanted. Whatever, there is a warning here, that attributing something to God does not give us free reign to impose on other people.
We should all remember that.