Ex still messaging me

Hey, so basically I broke up with my (now ex) gf 2 weeks ago or so, she did not want to but I just didn't see us going anywhere and did not feel like the relationship was 'healthy'; it mostly annoyed me and gave me unneeded stress.

I did not want to end on bad terms so I asked her 'friends?' and she sent me a thumbs up.

We then did not speak for a week and then she randomly popped up saying stuff like 'i dont know if we can be friends' and i was like 'okay then cool' and this dead conversation escalated to her saying she wanted to try again. I indirectly, but still very obviously, said no.
Since then she has been messaging me everyday with random stuff and trying to start conversations but I find it all very uncomfortable for different reasons.

Should I block her? I do see her at least 3 times a week so maybe that will make it worse?
Or is it my fault because I offered to be friends? And I should now live with it.
Btw might seem like a douche but I have reasons for not really liking her amymore... for example her sending pics of her chilling with boys all the time just to try and make me jealous, which I wasnt; I was just pissed off at her intentions.

Looking back on my post it was all very uninteresting for a third person so thanks if you read and care to comment.