No contact is the way forward. If she wants to get back together, she will let you know.
If you want to improve yourself, that's great, maybe you could read the relate book, stop arguing start talking? You should be able to borrow it from the library. However your focus right now should be on you. Sometimes, we don't realise we don't want something until it gets to the point when we are about to get it, i.e. after you talked about getting married, she might have started to see there was too much incompatibility between who you are and what she wants. Only she knows and she's not telling you anything, however it's about her, not you. She has to feel right about it.
So you need to get on with your life focus on you. If you think you did certain things wrong, like not listening, take action to prevent it in the future, counselling is a good option IMHO.
Good luck, stay calm, stay centred on you.
All the best,