Greetings @heather30 
I’m so sorry to hear that the new neighbors may have brought in some negative energy. You’ve got some great suggestions here from Amethyst and Francisco 
Adding to it, I’ve got a few more things you might consider!
Music is a fantastic way to cleanse the space as well as cleanse yourself too- you might also consider hanging a windchime 
somewhere where the air moves, as the sound of the gentle bell from time to time is purifying.
If the negative energy is outside your space, I’d recommend setting up a barrier 
. This is to make a clear distinction between the “outside” and “inside”- blocking off negative energy from coming into your home. This can be done in many ways, such as:
-
Drawing a line of salt across your doorstep and windowsill -
Hanging strings of prayer flags (either premade or made by you) -
Tying a talisman or charm on the door handle and hanging them from windows
I would also recommend casting a protective spell of your choice at timely intervals (once a day, once a week, once a month- however often you feel it is needed) 
As for your kitty- she may be feeling strange energy in the air as well as sensing your stress around the situation. My parents’ cat does the same thing- he is easily influenced by the emotions of the people around him, and when he gets stressed he does not like to be by himself 
If you’re in doubt, I would consider bringing her for a check-up to her vet .
Sending positive thoughts to you and your kitty- I hope you can get your home back to feeling homey! Many blessings 