Oh do I hear myself in your post!
When I was first divorced from my first husband, (my choice) I was scared, bored, and very very lonely. I'd never lived alone, and been in a relationship my entire adult life. I soon became aware that I needed to learn to be just me, me all by myself. I made myself do things I'd never done before, like go to an event alone, not even meeting anyone I knew there, just me. I met wonderful people and developed a confidence I'd never known before. It wasn't long before being single wasn't lonely or boring anymore. I could do what I wanted when I wanted, and I owed no one an accounting for my time. It was exhilarating!
I think everyone should have this experience, and learn how to just enjoy their own company.
IMO, I think what you're feeling now is transitional, you're craving what you once had and feeling a loss, learning how to fill the void with YOU. Until you're completely comfortable being by yourself, maybe it is too soon to invite someone else into your world.