Hey there. A couple of different theories are coming to mind as I read your post.
The reason there is a separation anxiety phase around a year old is because that is around when they start walking. Instinctually, with a new found independence, it is very important that they fear going too far from mommy. Since she just started walking, it makes perfect sense that her fear of being away from you is stronger. She will grow more confident with her new abilities and become less clingy eventually.
As far as the milk goes... at this age their growth slows down tremendously. I see my daighter polish off all her milk and eat all her food some days... and then go long stretches without drinking milk and barely touching her food. They know how much they need. They are so much better at that then us. She is probably at a growth lull and just doesn't need the milk right now. Keep offering it so when she has another growth spurt, it's available.
Also, by reading one of your other suggestions, I am wondering the same thing about your pregnancy. I am 5 month pregnant right now and a month ago my daughter (20 months) completely stopped hugging or kissing me. She outright refuses and gets mad if I try. She is still very affectionate to my husband and parents. It is a different behavior from what you are experiencing, but nonethless, her behavior has changed since I have been pregnant.... so it could be related.
So my advice is, not to worry and accept this as a phase with several different factors. Nurture her and make her feel secure and she will eventually move on to new behaviors with her new stages of life.