There are several older threads about similar situations that you can search out.
From your program's point of view, they feel you did not do well in your PGY-2 ICU rotation, and pulled you out because of clinical concerns. Just so we're clear, this is a BIG deal. It means that they feel you are functioning well below what would be expected of a PGY-2, poor enough that your performance in the ICU was dangerous. Whether that's what really happened I can't tell, but that's what they think.
In my opinion, the best way forward in situations like this is to:
1. Put you in a remediation plan. Make it clear what you need to do to get better, what the timeline for improvement is, and what the outcomes of failing to meet those timelines are. All of this should be in writing.
2. Part of the remediation plan might be considering outside evaluation and testing -- for psychiatric issues, learning disabilities, or other.
3. If I send you for an evaluation of a learning disability, I choose (usually in conjunction with you) whom will do the evaluation, and the eval is given to both of us.
4. I may recommend a psychiatric evaluation. Whether you get one or not is your choice. If you ask for help, I'll make sure it gets done in a timely fashion by someone I trust. In no circumstances do the results of the psych eval come back to me, or to your file. If the Psych eval feels you are unable to safely practice for any reason, then they put you out on medical leave (which they obviously tell me about, but not the details/reasons).
I do agree with the above -- if you see someone and they label you with an illness, that does add some level of protection as you are then covered by the ADA and the program must make "reasonable accomodations" to manage your disability. But having your PD have open access to your psych records is a really bad plan, IMHO. That said, if they are demanding this, then there is little you can do -- either agree and see where it goes, or refuse, potentially be fired, and then consider lawsuits etc -- a long and painful road that often leads nowhere.
Bottom line:
1. Ask if the psych eval is mandatory or optional.
2. If mandatory, ask if you can see Occupational Medicine -- or perhaps go to them directly on your own. Hopefully you can convince them that pt-dr confidentiality attaches, and that they can't speak with your PD without your permission. Make this explicitly clear during your visit. Then you can have Occ Med help decide whether you need a Psych or other evaluation. This assumes your institution has an Occ Med dept, which it may not.
3. ACGME rules will not help you here.
4. Be very aware that this is the first step in your possible termination. It has nothing to do with the psych eval -- it has everything to do with your poor performance in the ICU. You must figure out, hopefully with your PD's help, a path forward where your performance improves.