Did I do something wrong?

Alright this is gonna be kinda hard to understand because I suck at describing past situations but I’m gonna try.

I was walking back home from a job interview at the grocery store a few days ago. As I made my way out of the grocery store parking lot and onto the sidewalk built along the main road I noticed I was approaching a lady that was walking in my direction. She decided to jay-walk to the other side. I thought nothing of this. I had to go in the same direction she was going but I didn’t know she was headed to the same place I was headed until later. Anyway, after she jay-walked across I paid no further attention to her, I went on about my business. I get to the intersection and press the button to cross. I would’ve jay walked across a lot sooner too but I’m on probation and don’t want to ruin the progress I’ve made so far just because a cop may decide to cite me for jay walking so I decide to cross the legal way even though it means a little more walking. So I get across and continue walking home. A few minutes into my walk back home I notice the same lady from earlier is walking several yards ahead of me in the same direction that I’m headed and when I say several yards I mean like at least 65-70 yards ahead. At this point we’re both walking in the suburban neighborhood where I live. So far everything seems normal. Well she started looking around and then eventually looked in my direction behind her. She holds her glance for a few seconds and then turns around. She keeps looking back at me several times as I continue walking home. I get the feeling that she thinks I’m stalking her so I slow down a little so as to not make her feel uncomfortable. I know it’s not my job to ensure she feels comfortable but I do it anyway even though it’s a little inconvenient for me. So I continue walking and she keeps turning her head around to look back. She eventually decides to cross the suburban street to the other side that has no sidewalk and continues walking but now she’s walking on rocks. After she did that I felt like it’d be cool to revert back to my original walking speed and so I do. I eventually pass her and continue walking home until I got home.

Am I overthinking this situation? Did I do something wrong? I was even considering sitting down at a bench built along the sidewalk so as to give her time to get more distance but I didn’t because she was several yards ahead as I said earlier. It was broad daylight too, other people were walking around nearby, and cars were driving by. It’s not like this was at night time in some dark alley. Does a woman’s paranoia of men warrant a response from men in the manner that I decided to go with? Should I have to walk on eggshells to this degree around women?

For the record: I realize women are more likely to be victims of rape, please excuse me if I sound insensitive to women. I posted this question so as to get other people’s opinion (men & women) or advice on the situation as it’s a situation I have found myself in before in the past.