This is not a case of shooting the messenger.
Shooting the messenger would be if your boss treated you based on how he feels about the message you conveyed.
A border guard stops a civlian at the border. He kindly tells the person that the local government has decided to close the borders to people of this civilian's nationality.
As a response, the civilian shouts (or attacks) the border guard.
This is an example of shooting the messenger. The civilian is taking his frustrations about the new law out on the person who informed him of this law. The border guard is the messenger, he is not responsible for passing that law.
In Dutch, we say "don't shoot the pianist". It refers to the Wild West stereotype where someone would shoot a pianist for playing a song they don't like; when in reality the pianist is only playing the songs that he is told to play by his boss.
You can argue that this is similar to people e.g. shooting or attacking their TV when they don't like the news message that is broadcast on the TV station.
Edit Reading my answer again, there is one case where this can be considered shooting the messenger: if your boss' response is basically "well if you're going to contradict me, YOU deal with it then". His response is a punishment, enacted on you for conveying rules that you did not create; therefore shooting you as the messenger of these rules.
So what do you say instead?
You still need a way to talk to your boss. I'm struggling to find any idiom for this, so instead I'm going to rely on non-idiomatic communication.
If I were put in your situation, my response would be something like
I only wanted to add to the discussion, rather than take over.
You can then follow this up with a reason for why you don't want to take over. This is very personal to you, but from what I gather from your question, it would likely be something like:
- I already have a full workload and cannot take this on top.
- I am not the person who you need to talk to about this.
- I cannot help you any further with this issue.
These are all relatively polite ways of dealing with it. If your true reason is less-than-polite, e.g. "Why do I always have to pick up everyone's slack?", then I would suggest you talk to your superior and let them handle it on your behalf.
That is what a manager does. They manage the workload for their employees, which also includes addressing any issues you are having with your work, even if they are personal objections.
But my manager is the person sending me this work!
To be frank, as a manager, he is supposed to be able to handle that. He needs to (try to) assist you with any issue you have, even if it is an issue pertaining to himself.
If he is incapable of objectively trying to help because he feels personally offended (which can be considered shooting the messenger, funnily enough), then you should take it up with his boss. However, I do suggest that you talk to your boss first, to not offend him by immediately going around the chain of command.
Any further tips on how to approach your boss should be posted as a question on Workplace.SE, the site is much better suited to this kind of problem.