Hi Springy,
I am not an expert in any way but here are some thoughts from someone who has spent some time thinking about things like this:
the health professionals are the best qualified people to treat mental health problems, so yes, consult them. however, they are not necessarily the best qualified to distinguish, in you, between feeling crap as a healthy person in crap circumstances, or feeling crap as a depressed person in any circumstances, or what point you are on in the continuum between the two.
To some extent it can sometimes be a personal decision on your part how you want to approach this. It can be useful in the short term to put it all in a box marked "mental health issues" and treat it like that if you are not able or currently willing to change certain aspects of your circumstances. Certainly there are some very difficult aspects of looking after a small baby that cannot be changed and I see that as being a significant component in the usefulness of the "mental health issue" approach - alleviating some of the crapness of how you feel without trying to change the world, which is impossible.
However, there may be some aspects of your circumstances you can change - now, soon, or further down the line - even perhaps some aspects of baby care (does your baby ever take a bottle, to give you a break? Is it possible with your baby to introduce or tweak a routine so that you have some fairly reliable sleep times, if you don't already? - just thoughts, I don't know, and all babies are different). I would guess - and this really is a guess as I am not a medical expert, nor do I know you - that your situation is one that may benefit from a real hard radical look at what there is in your life that is good, bad, or indifferent, and what there is in your life that is subject to change and what is not.
Part of the reason why I suggest this is that you seem, yourself, to be separating your negative feelings from your baby - as if you have already drawn a mental line between "things that make me feel crap" and "good things and ok things" and the baby is not on the crap side. Therefore I would suggest that you know in yourself this is not PND, or not just PND uncomplicated by other mental health issues or other life circumstances, but for various reasons it may be convenient to assume it is PND, and treat it as such; and as you have just had a baby, this "option" is open to you; and this is something that does not require you to question other things.
BTW, again as a total non-expert, I think there is nothing at all dysfunctional about not over-worrying about your baby - quite the opposite, that is a balanced attitude to congratulate yourself on.
Finally, I am not meaning to imply at all that PND or any other mental health issues are "optional" or simple - they are very very real and sadly not in slightest way chooseable. I just think that there are societal and personal motivations, as well as medical factors, sometimes, in the way in which we go about negotiating the interface between personal circumstances and health.
Read "sunbathing in the rain" by Gwyneth Lewis: she draws a very strong casual link between a failure of honesty to oneself and depression. So, conveniently, though horribly, treating something as depression whether or not it is will ultimately have the outcome of it being depression anyway. Arguably.
Sorry if this is just waffle. I wish you all the best for things improving. And it sounds as if you are a great mother.