If you're interested in change and more importantly self-introspection then you are not a complete psychopath. Self-introspection is pretty inconsistent with psychopathy as well as most personality disorders in my opinion. (I don't acknowledge that word exists) so let's just use it interchangeably with personality disorder.
You say you want to change bits and pieces and then you say you don't want to change. Which is it?
There are general criteria to have a personality disorder BEFORE you can have a specific personality disorder.
http://en.wikipedia.org/wiki/Personality_disorder
(diagnosis area). So I ask you. Is there significant interpersonal dysfunctional, social and/or occupational dysfunction that has existed almost since as far back as you can remember?
If you are struggling with non-PD issues like depressive disorder, bipolar, etc then you should seek out treatment and also bring up whatever issues you are having in your life. That will probably be handled with medication.
I spent one time inpatient a few years ago for a suicidal ideation. Someone put me in there (my friend, I was not in therapy nor was I ever) and in there I was diagnosed with depressive disorder NOS. Being inpatient was annoying and a waste of my time. It depends on what hospital you're at because the first one I was at before I was transferred was a nightmare. No one is going to send you away unless they think you are an immediately threat to yourself or other people.
My axis II (where personality disorders go) was deferred upon my discharge. There are things in the way I think/behave that are taboo. I really didn't realize that then, and on a good day I'd say I have maybe 65% self awareness. I'll let myself pass. There's thing I will probably never see. There's parts of me that I don't understand the root to nor do I give a crap.
I have recently gone to therapy for the first time, as I was not required to upon my discharge. Like you (or maybe not you?) there are parts of me that I would like to change. There are parts of me I am not interested in changing. I don't fit into any specific personality disorder, but PD-NOS so it can kind of get messy. I don't lie in therapy, there are somethings I won't discuss but I won't lie. I'm actually very honest and for being a person who has significant PD issues (evident in social and occupational dysfunction) and I vocalize what I think maladaptive behavior behind that a lot of the time. Lying is BS if you don't have an ulterior motive to enter treatment. If you're an attention seeker that's catering to your disordered behavior.
/end rant
Most of the things I won't discuss are related to behaviors I am not interested in changing so it's absolutely pointless to discuss them. Is therapy helpful? I have someone that understands and we are a good fit. But if you do have a personality disorder it is very hard to change the way you think and it takes time. And to be honest sometimes it's impossible.
Hope you understand a little more and can make a little bit of a more informed decision.