Hi Mila,
Yes, there are people who have experienced this situation after having met someone on a dating site. It is never good when a person refuses to send a pic, especially after a good month of consistent communication with a dating prospect.
You made the right decision in ending it when you did. She was secure enough to create a dating profile and put herself out there. Now that she has had time to build some rapport with you over the course of a month, she really has no justifiable excuse to refuse to send you a pic of herself.
Catfishing is something that is unfortunately very prevalent in online dating. People pretend to be who they aren’t or hide their identity in the hopes of luring unsuspecting prospects into their web and taking advantage of them however which way they deem beneficial to themselves alone.
After you ended it, she has continued reaching out to you because she isn’t ready to sever the connection. She has come so close to getting you to where she wants you to be, completely in love with her.
You have already experienced some of this in how you recognized that you are falling for her. That is what she wants.
You shouldn’t respond to her messages. If you do, you will only find yourself drawn deeper into her web of deceit. Block her from all forms of communication and move forward with your life.