How to avoid uncomfortableness at work with co-worker you don't even know?

Right now I am working at a call center and for the past week I have been sitting in this same seat because I like the spot it is in. Today I come in and there is no seat at the desk so I grab a seat and slide it over to that desk. While doing this I could feel the woman whom was sitting next to me watching my EVERY move so finally I look at her and say "good morning". She says it back but in a nasty way. Fast forward to lunch same lady is in the lunch room standing by the sinks. I put my lunch on my table and go to get some paper towels to wipe off my table with. This woman asks me "are you following me?" and I laugh because I thought she was joking. Surely she cant be serious right? Well turns out she was because when I got to wet the paper towel to clean my table she proceeds to say "I just want to know, you sat next to me this morning and now you are in here with me. I'm not really comfortable with that it's a bit creepy." Now when she said this I didn't even respond I just continued to laugh and walked away. I then see she quickly grabbed her things and moved outside of the break room peeking in to see if I am at the sink and paper towels and then finally coming back in to finish up whatever she was doing with her lunch. When I came back from lunch later thankfully she had moved her seat so I didn't have to move mine to avoid anymore awkwardness that day. I am still so taken aback as to how and why she would jump to such a wild accusation I think I have seen this woman