Op!! You poor thing, its hard to understand the FEAR if you have never suffered from selfish, evil neighbours, of course your going to be worried.
First of all, loads of smiles from YOU, big bunch of flowers and chocs from YOU to her,....welcome to new home card from YOU, with note in it, to say if she needs anything please knock and dont hesitate.
ALSO PUT IN NOTE, I have lived here for a long time, and I must apologise in advance for any noise MY SIDE you may hear, please let me know if the telly is too loud etc....
DO THIS OP, DO IT DO IT DO IT.
She will think you are a lovely person, and wont want to upset you and will be much more open to you - if you knock and very sweetly tell her the telly is too loud...or smoke is coming in.....
The absolute KEY in these situs is getting off to a good start.