This Situation With My Ex Is Killing Me, Any Advice Please?

4 months ago, my ex girlfriend split up with me after 1 and a half years. Long story but it seemed very sudden and she used reasons like she doesn’t want to settle down, she needs to sort her career out, she wants to do stuff spare of the moment and she wants to find her own friends again. This was fair enough but I never stood in the way of her doing this and she knew I didn’t want to settle down yet as were still young, I’m 22 and she’s 21. This was all triggered of by a slight argument we had a week after her 21st birthday and then she said she needed space and then she basically dumped me by text message.
We did meet up a few days later to clear the air, she wasn’t going to take me back but she said maybe in the future. She said she’d been meeting up with friends including her ex who cheated on her 2 years before she met me, but they were friends afterwards. We left it at that and left on pretty bad terms. A couple of days later she blocked me on facebook but remained friends with my brother and I remained friends with her family. A week or so later, her sis-in-law posted a pic on facebook and it was at a party at there house and I noticed her ex was also at the party. I felt terrible and I feel terrible for doing the next thing but I checked her emails as she had given me her passwords. I found 2 emails to her ex one saying ‘I miss you’ and he replied saying ‘I miss you too, I hate Mondays after our weekends together’. This was 2 weeks after we split up but she doesn’t know that I know about the emails.
I decided to take peoples advice and not even contact her and cut my losses with the money. We didn’t have contract for about 2/3 months until 2 weeks ago as her gran died. I knew this as her brother posted it on facebook. I decided to text her and say I was sorry to hear about her loss and my thoughts are with her family. She replied saying thanks hun x. I left it at that and then a couple of days later it was my birthday. She sent me a text saying happy birthday x and I just replied saying thanks. And then she replied saying have I got any plans this year and I replied with a few things like I’m going skiing and starting a degree soon and asked her. She said shes got some job interviews and her grans funeral (this was about a week ago). We sent a couple more texts, I showed her sympathy towards her gran and said well done for the interviews and then didn’t hear anything else. Although it looks like shes unblocked me on facebook as I can see her comments on her brothers wall and her relationship status says single (so I don’t think shes with her ex).
Since then, my minds been going crazy and i’ve been going through hell since we split. I’ve tried so hard to forget her but she just doesn’t leave my mind, I think about her all the time. I’ve been going out with friends, joined a gym etc but nothing seemed to be working. I do still care about her and love her to pieces, I don’t know if she knows this and how much she hurt me as I didn’t beg for her to come back or anything. Did I do the right thing? I’m so tempted to contact her again to see how the funeral went and the interviews but I just don’t know what she thinks about me. Maybe she thinks that I’m not bothered about her, I don’t know. Or if I do contact her she will probably think I’m weak and waiting for her. Does anyone have any advice for me about this mess and whats the best thing to do?
Thanks for reading, advice will be appreciated greatly.