Firstly, your new psychologist should not be convinced you have ADHD unless they've assessed and diagnosed you with ADHD... Until they do so, all they've got is a suspicion, and if they were skilled in the area they would be doing the assessment and diagnosis themselves! It's called scope of practice. It sounds like you have had someone skilled in ADHD assess you and they thought you didn't have it. The idea that your boss, who's not an expert in ADHD, let alone done a formal assessment of you, is capable of diagnosis is laughable...
Sub-syndromal means that you have some symptoms but not enough to meet the criteria for the disorder, or that the symptoms you have are not severe enough to meet the diagnostic threshold. Does that make sense? Do you know how the DSM diagnostic system works? There's a list of diagnostic criteria, and if you meet some but not all, you'd be considered to be sub-syndromal. (That's not the only way drs make diagnoses, but it's the simplest.)
My sense is that things are not working for you, and you are wondering if an ADHD diagnosis would help. Diagnosis only helps if it leads to appropriate treatment. Personally, if I was you, I would be happy with the description of subsyndromal ADHD, and work with my psychologist on all the strategies that people with ADHD use to manage their symptoms, if you think it's a problem. There's a heap of psychological strategies, and if you think your ADHD features are getting in your way, start learning to use them! That's what your psychologist is for. If I had subsyndromal ADHD, and I thought it was getting in my way, that's what I would be doing. There are ADHD coaches around, try one of those if your psychologist is ignorant. It's a specialised field. You don't need the diagnosis to go and see one, subsyndromal symptoms is perfectly sufficient.
Think of bipolar 2 as subsyndromal symptoms of bipolar 1... Hypomania is subsyndromal mania. I don't know if that helps the concept make more sense. Bipolar 2 is a relatively recent invention.
Hope I've helped.