How to cure myself from being jealous or should I try?

I've been dating a guy for 2 years, he moved in 6 months ago. He said he was out of a long term relationship for 2 months when we met, but he left valentines from her laying around, and still paid for her cell phone FOR 1 YR INTO OUR RELATIONSHIP AFTER SAYNG HE WOULD GET IT BACK AT LEAST 7 TIMES. He said they are just friends and he hasn't talked to her in 9 months. So many things were left out for me to see that now I don't believe him and obcess about them together and wonder if he loved her more. He even said he never would have kicked her out if she hadn't told him to go and be happy. She is supposedly sick but I think it is combined with addictions to prescription drugs (saw lots of narcotic pill bottles with her name on them). Anyway I feel bad very often because I do love him but lost my trust since he lies about her whenever I bring something up. like her number wasn't on his cell when actually he had it under a man's name. I turned into an obcessive snoop too. He claimes to love me and we are together all the time and do enjoy ourselves except when i get jealous.