I recently started talking to an awesome woman online - not OLD, just random happenstance - and we really hit it off. I messaged her every single day for a couple of weeks, started to have the same doubts as you, and told her that if it's too much and I'm being annoying, I don't mind dialing it back a bit. She said she had no complaints and would let me know if she needed some space.

We chatted for hours every day, for months. It's died down a bit lately, but we still chat more days than not. I probably still initiate 80-90% of our conversations, but I'm no longer insecure about it because we discussed it and I know how she feels about it now, instead of just wondering. Maybe this could work for you too.