Ok, I'm going against most peoples opinions on this but this is only my point of view. Of course everyone has different personalities & communicate differently but op I just see that as a friend who's genuinely interested & excited for your pregnancy.
My friends & I are like that & even more so after having babies. We would all text each other after scans making sure everyone & baby is ok. We've all been through miscarriages & had other things happen during scans where it's nice to have that support afterwards. We also regularly Facebook chat even though we may have seen each other at work. But that chat is about things we haven't been able to talk about at work. They have been such a godsend for me after having my dd. They've been there to Facebook chat too in the middle of the night when baby won't sleep & on bad days when I needed a vent. They've been great for advice & support & I would've felt so lonely without them. We all get along & have similar personalities but I've also texted a friend after I knew she's having a scan (although I'd stop at the one msg).
Anyway, that's only my experience with my own friends. I hope you can work it out with her She may not realise she's come across as overwhelming to you when she may only have been trying to show an interest with you & your pregnancy.