Oh pendulum, I have to respond to this but excuse typing as DS is currently on my shoulder whingeing.
I can identify so closely with your feelings of anger and frustration. My DS is 4 months and very, very like your DD. I've shouted at him, walked away from him, slammed doors, punched walls, wept, screamed, you name it. It feels at times like he's testing me, as if he's waging a campaign against me, although logical me knows that to be impossible. I have pent-up anger and short patience. I feel like I'm all out of sympathy for him, sometimes.
I spent a long time questioning whether I am normal, whether our bond is normal (there definitely is a bond - like you, I don't like being parted from him and I feel possessive), whether it's "OK" to feel this anger.
I think sometimes people get babies who give them a rough ride, and certain combinations of parental personality and baby's demeanour can result in this rough ride becoming a deeper resentment. I've posted loads on MN for help with various sleep/wind/crying problems and been reassured that my baby is normal, and that my reactions are normal - it's just we have landed difficult babies.
Things are better now DS is getting older, although the anger is still there and I know I need to find patience every day. But I take comfort that before long he will have other ways of communicating beyond wailing, and he will be better at falling asleep when he needs to, and the wind will settle down. It won't be like this forever. Some good advice from another mumsnetter was to put on a veneer of "calm parent". It's just an act but if you can do it you'll find an extra few minutes of patience which is often all you need. I also consciously lower my expectations - I go to settle him and tell myself it will take 2 hours. These days it can happen much quicker but I check the clock first so I know how long it is taking me (often less time than it feels). This helps prevent me becoming frustrated too.
I understand why you can't talk to people in RL (my DP understands so I am lucky in this respect, and my mum had 3 babies like this and has been very supportive, but I don't feel I can talk to my HV about it), but if there is an element of depression then maybe you should try finding someone to confide in. I worried about this but I do feel it is mainly tiredness and the sheer frustration of having such a difficult baby to deal with all the time.
On a practical note I too would recommend a sling, it's been of great use to us. And also just believe it will pass - as the good times increase in frequency, the smiles become giggles and the crying abates I am finding the situations in which I feel real anger are much less common. As I said before, soon we will have so many other means of communication that it will be much easier to find problems and deal with them rather than this infuriating battle of guesswork and trial and error.
Keep posting on here, it keeps me sane!