My coworker does not stop talking?

My coworker works closely with me and does not. stop. talking. I've never seen her quiet for more than a minute, she's constantly talking about her love life, personal problems, her political views, basically everything. And here's the annoying part, she follows me everywhere! She's like glued to my arm, I'll go around the corner to get something and she's right next to me following me while talking about something. I'll try to clean something or organize something and she's following me around while in doing this just talking. She's said to me that she doesn't have an friends and doesn't have any one to talk to, but she shouldn't be doing all of this at work. I've hinted to her that I'm annoyed from her talking by not saying anything back or just being like "uh huh" or "mkay" But she doesn't get the hint. I've mentioned to my manager that she follows me around and my manager isn't really a problem solver, she just says she'll talk to her and give her chores to do but she never does. Right now where we work, it's slow so we don't have a lot of customers so that's why she's talking so much to me, but there's always stuff to do. I clean when it's slow, she just stands around and talks. I've been thinking of how to politely mention to my coworker to stop throwing talking but I don't want to come off as mean because she's very sensitive and I feel like whatever I say, she'll be offended. Any advice?