Oil burning

The code may have been for the EGR but that is most likely not going to mean it is blocked. That is one possible cause but if it was just replaced, then it is unlikely the issue and there is another issue with the EGR.

However, we need to start with finding out what code is there so that we can work through that issue.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

As for the oil burning that, could be related to the EGR issue so we need to start with that.

https://www.2carpros.com/articles/blue-smoke-from-engines-exhaust

However, if you are burning a large amount of oil, then that could explain why they say the EGR is stuck so again, we need to start with what code is there and go from there.

Thanks