I think he's not over his ex girlfriend yet?

I will try to keep this short,so I was 2 months together with this guy things were going great the first 2 weeks,he even told me the second day I was with him that he's ex girlfriend still came over but not to see him but she had a great bond with he's mom and they go to the gym together every Thursday.they were together for 5 years and it was done for 6 months when he started something with me,so he told me I don't have to worry because it's done between them,he also told me after 5 days he wants to have me in he's life forever and was never gonna let me go.anyway after 2 weeks he started to comparing me with her and he talked about her sometimes,he also started to pull away,but this was because while I was with him my mother find out his cell number and texted him to leave me alone,it drove both him and me crazy,it's none of her business who I date,so I could tell it was really affecting us as a couple, the last week he was really distant he send me text messages that he couldn't see me because he was tired so I asked him are you having doubts to go on with me he replied "did I ever told you I want this to end?" but then 2 days later he called me to say he was having doubts to go on and I could tell by his voice he was irritated.so I said it's better to end this now if you're having doubts and he didn't replied on that one so I broke up with him and said it's best if we stayed friends and after a few days he agreed to stay friends,but than I started to have doubts did I do the right thing by ending this relation? I mean I thought it's best to give him some space but it's been more than a month ago and I didn't heard from him so guys or girls what do you think should I talk to him about this because I really want him back or need to give him more space to think?

Also is 6 months enough time to get over someone who you been together with for 5 years?
I think he's not over his ex girlfriend yet?
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