You may have broken up in January but it wasn't until this week that you accepted that it will never be like it was before. That makes it only a week or so that you've actually and sincerely started on your journey of getting over her romantically. That's not your fault, she gave you mixed messages and dicked you around for a long time (cause she's got mental problems as far as I'm concerned). Your only mistake was putting up with her push/pull crap and not just telling her yourself that it was over and over for good. Tell yourself that now, believe it and it will help you to get to the next stage. You will leave one stage and likely revisit it and then move to the next and go back to that one as well. Getting over someone is a process, it's not an event and it takes time and using your time well to move on quicker.
Once you're a little more indifferent to her and what she's doing (more at a point where you don't care one way or the other) then you'll be more open to dating and having opposite sex fun. Don't worry about learning to live happily alone. Once you can do that then you're going to make a better partner for someone and you'll choose more wisely as well.
What you're experiencing I think everyone on this board who has been in love has experienced. You'll be fine if you don't stagnate in your current phase so do the best with your time and keep busy, learn to appreciate the time you have with yourself and soon you'll be back out there once again.
Choose wisely next time and where a rubber. No more having children with issued women who don't have a clue what they want, who you hardly know and who turn out to be nuts.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion