The relationship you two had doesn't sound like it was very healthy. If you two were arguing so badly you'd have to break up and get together... That's just not how a healthy relationship flows. My husband and I had some bad arguments before we got married and a few afterwards (we've only been married for a year), however, after arguments and cooling off we would always always get to a point where we could reconcile and we never had to break up in order to do that. We always hit a point where we realized the the argument wasn't worth it if we truly loved each other we would end up focusing on our love and willingness to fight for our relationship and not be each other's enemy. When your involved in an unhealthy relationship it tends to get out of hand to the point people break up and then when you get back together you jump back into things without truly solving or working on the issues and it's only a matter of time before it happens again.. like a roller coaster!
I think it's best for you to focus on moving on. I also see that you are acknowledging the fact that you have jealousy issues and that's a good start! I'd recommend really working on this within yourself before you begin dating again. Unfortunately, anyone you meet or date is bound to have a past of some sort. It's a bit unrealistic to think that you'd be the first person they were attracted to or dated. Plus, you have a past as well. I understand being a little jealous because I think that's a very human reaction but you have to learn how to deal with that within yourself in a healthy way and to work on how you perceive a person's past and respect it.
I understand you got close with her daughter and sometimes that it one of the rougher things to deal with during a break up. I have an ex, who is also the father of my daughter (now 11), I was with him for a little over 2 years and I was really close with his older daughters. Since I had a child with him and those girls were my daughter's sisters I chose to be involved in their lives even after we broke up. I'd see them at least once a month on weekends and such. I did have to reach a point when they got older to set my own boundaries so that I wouldn't be going over and beyond my own mental capacity for children that weren't mine. I did this for other bigger reasons that involve a lot of drama and such. In your case, you two were never married and don't have kids together and as hard as it is I'd probably recommend cutting those ties with the daughter. She has a father and she is young and if her mom eventually moves on and dates someone else that relationship will likely change and be too complicated.
If it's possible to change jobs I'd make it a goal. If not, just work really hard on yourself and find new people to associate with even if it's outside of work. Take up some new hobbies. Maybe get some counseling to talk about things and work on your goals for yourself. Concentrate on what you can do to better yourself and gain more confidence! You got this!