Hear me out!
I took my 6 month old LB into town today with my BIL and niece. He needed to run an errand before we went for a shop and my little boy needed a feed so my niece and BIL left me at a coffee shop so I could park up and feed my lb.
A lady who I have seen before locally (I dont know her personally) was watching my lb and myself really intently as I walked in but I didn't think too much of it. I ordered my coffee and sat down at a table directly across from where she was sat as it was the only place where the chairs didn't have arm rests ( I'm ebf so they get in the way of my little boys legs). I had my lb out of the pram and was almost ready to feed him when I realised she was still staring at me. She never looked away- not even when we made eye contact with one and other. It wasn't subtle at all and made me feel really uneasy and I was deeply unsettled so I moved to a different spot with my little boy that I had avoided due to it being an awkward chair to feed in. She was still watching me in our new spot ( baring in mind I hadn't started feeding and she couldn't have seen anything like a breast/ nipple- not that that would be an excuse to stare unblinkingly at someone!). I ended up blocking her vision with my pram but could still see she had her head turned towards us.
My little boy had finished his feed and I was enjoying my coffee when she walked past us to go to the loo. She pointedly turned her head to stare at us as she walked by and only stopped looking when she had physically gone too far to be able to turn her head enough to see us. She left and my BIL came back and I told him about the weirdness of what had just happened.
Scrolling through Facebook I noticed someone else who has been in town today (not someone I know) had posted about a lady of the same description following her and her young baby out of the bus station. I messaged the lady to tell her about my experience with what I thought was the same woman. Apparently this woman had been on the same bus as her and followed her, complimented her on her 'beautiful' baby and was getting herself very close to the pram (the lady with the baby told her to go away). She continued to follow her until she was again told to stop and leave them both alone. This lady also noticed she appeared to be pregnant but with an almost too perfect looking baby bump (which lady with baby suspected may have been fake). Shes been reported to the police by this woman as her social worker (fostering) suggested it may have been related to gangs trying to snatch babies 
and she has suggested I also report how she was behaving in the coffee shop.
It feels weirdly reminiscent of a bit too many crime dramas/ true crime shows where women have faked pregnancies then snatched babies. The thought of someone with a baby meeting this woman in with no one around makes me feel a bit sick.
I feel like I should report her as the experience of this other woman has turned what happened to me today from something a bit unnerving to something that now feels very sinister. I do feel like I'm going to sound like a mad woman calling the police to report someone for looking at me funny though!
I hope this makes sense as I'm rubbish at being concise.