Agree with pps to stop picking her up. She’s biting harder because her more subtle signals (stiffness, whale eye, lip licking) and previous attempts at biting which were less forceful, haven’t worked. Effectively she’s been forced into biting, as her last line of communicating how much she hates it.
Make the alternative to what your distracting her from so amazingly tempting she can’t possibly resist (roast chicken, Arden Grange Liver Paste, a handful of hotdog pieces scattered across in front of her) or get her keyed into a particular toy that she will reliably respond to, one with a really good squeak if possible and then keep that toy as an A grade reward, instead of letting her have free play with it.
We have our first toy breed after a lifetime of large dogs and it’s been a real learning curve. I am determined mine will not be a ‘handbag/carried everywhere’ dog, but I was surprised to find you do instinctively go to pick them up a lot and have to remind yourself not to. What may be useful is looking up Kikopup’s YouTube video on training small dogs to enjoy being picked up. That way, when you really do need to do it in an emergency you will have the option without it upsetting or scaring her.
As for getting her off things she shouldn’t have. Rather than focussing on removing her physically, I would train really strong, reliable leave and drop it cues, so that they become instant and instinctive to her. I tend to think, if you can train a dog drop things, leave things, come back when called, instant down, settle and walk with you on a loose lead (not necessarily a perfect heel, just nicely next to you without pulling or dragging) you have the ability to navigate most worrying/difficult situations safely and effectively. So these are the things I focus on first with all my pups. (For recall we whistle train and you can then use that to call them off things they are getting into but shouldn’t from a distance.) For me, sensible but reliable basic control, while still allowing the dog the freedom to make choices is the basis of a good relationship and helps to build a strong bond and relationship.