It sounds like you're in a spiral and its hard to say which came first, clingy child, sad mum, fed up dad. It doesn't matter really.
You sound like you are mildly depressed, understandable, lots of people are when they have small children as it is such hard work! Mine are a bit older, I am in a bit of an overwhelmed phase myself at the mo - life is so busy, my eldest only four but at school with all the organising that entails, and my youngest is 2.5 and its like living with a (very cute) Roman Emperor.
First off, children have miserable phases when they are just, well, miserable. I remember 18 mths being grim with my second, I think he was cutting his first molars, sleep went to pot, intense separation anxiety. Don't take it as an indictment of your parenting that she is only miserable with you. If anything it shows the strength of her attachment to you. It means that you have succeeded in creating that bond with her, which is the primary goal of the first two years and the most important thing of all. It doesn't seem it but her protesting at separation from you is a sign things are well.
If she is miserable it is probably teeth and/or something developmental going on, she is probably about to get going on words, and whenever they are about to do anything new it can wreak havoc with sleep.
Little ones also have the most incredibly sensitive antennae and they pick up your mood like a Dyson. If you are miserable and down, she will be too.
Before they are two ish you just constantly cycle from good to bad phase, what with teething and developmental leaps. Its impossible to keep up and can be stressful. You're in a bad phase at the mo. But in three mths time, it will be summer, she will be closer to two, things are very likely to settle down until you hit the full on twos at about 30 mths .
If I were you I would see my GP to see if you could get some mild A-Ds short term. I would have a heart to heart with my other half, acknowledge that you are both feeling miserable and try and work out how to make things better and remember what brought you together in the first place.
And I would think about what is the best way to get through the day with a clingy child (for me it was going OUT, my two were much less whiny when out, perhaps because we were always together and they felt safe, and also stimulated and not bored).
Good luck. It will be better as she grows up. Its especially hard first time round (is she your first?) as you can't see the next stage coming up. But soon enough she will be trotting off to preschool with her book bag, potty trained, telling you jokes and being such fun. It's only a year or so away, try if you can to enjoy what good bits you find of this age as soon she will be much more independent, a really separate person. You might even feel wistful for how she was at this age! 
Good luck.