Should I call someone if my ex threatened to commit suicide after our break up?

I broke up with my ex of 6 months a week ago. He's sent me multiple texts saying he was going to kill himself. I don't know if he just saying it for attention because he's very manipulative or if he's being real. He's very unstable and I've always told him he needs to talk to someone about his issues from the past with his family and relationships but he hasn't. I know he has abandonment issues and feels like no one loves him. It was like he ate, slept and breathe me. He smothered me. He was one of those what are you doing after work? What are you doing after that? What time will you be home? Text me as soon as you get home. I wanted to scream half the time and I actually did most of the time. I would try and talk to him and tell him all that wasn't necessary but he never really got it. He'd text me and if I didn't immediately text him back, he was calling me on the phone, not even giving me a chance to reply to the text. This happened constantly. He was clingy, needy, emotional, sensitive, jealous and insecure. He was always worried about losing me to another guy because I was so pretty and he felt lucky to have me. No matter how much I tried to reassure him and tell him he didn't have anything to worry about, he still worried. All these things were a big turn off for me but felt so bad and guilty I wouldn't break it off but this past Holiday weekend he got out of control and I had enough and told him it was over. He sent me countless text messages going through different emotions, he hated me, he loved me. Just tell me to move on. I want to see you face to face to talk. I found someone else who's going to make me happy to begging me to call him and talk. After I got all of those texts, I blocked him from texting and calling me. I have no idea how he's doing. I do care but can't open that can of worms again, he'll think we're getting back together or something. Should I call some mental health facility? He's very unstable and his family could care less.