Why does it make me anxious when I confront someone?

The anxiety is primal.
Predators stare. They size up most every creature they see. Is enables them to decide what is worth chasing, and whether they have another predator in the area which will compete for the same prey.

That is why people, and animals become uneasy when they are being stared down.

You didn’t say why she harassed you in the past, so there is no way for any of us to predict whether she will again.

What more do you expect her to do?

You don’t like to be confrontational. There are times one has to be and then one hopes to get their point across peacefully, and understandably, without it becoming some big deal.

Stick around here and we’ll help you learn to enjoy confrontation as well as feel safe doing so. Physically you may need to learn to protect yourself so you aren’t afraid.
And unless you are ready to stand up for yourself, stay well away. Avoidance. No eye contact.

It’s this
This can help calm you,
Looks like you’ve won that round, btw :)

“A lady who lives nearby (who used to harass us) was staring at me from her car a few yards away.”
Fear mongering is what she is doing.

Because it IS someone who used to harass you. All the old feelings come back to the surface.
Normal feeling for someone who had gone through a traumatic time before.

Is she stalking you or was this random?
There are laws on stalking.

@inspired_2write just a random coincidence. Thank you. That possibility didn’t occur to me.

Most people don’t like confrontations, myself included. It’s the unknown, you have no idea what the other person is capable of.

@AshlynM yes I feel the same