Is it bad to care too much?

My boyfriend is in the Air Force and he recently told me that he gets depressive episodes. So, on Tuesday afternoon he all the sudden stopped texting me and wouldn't answer my phone calls. I became concerned. I thought maybe something happened to him like maybe he was in a car accident or he may have committed suicide. He didn't contact me for a whole day and a half and that's just not like him. So, I called his unit and asked if he was at work. I just wanted to know if he was there because that would let me know he was okay. They  didn't even know who he was.  He called me 10 min after I called his unit on base and he left a very angry voice message saying I put him in a very "embarrassing" situation and that I made the whole base to a search for him and even the security officials thought he was missing and that if he wanted to talk to me he would and if he didn't he wouldn't.  His excuse for not contacting me was that he was busy, I told him it doesn't take very much of his time to send a text saying "hey babe, I'm busy. I'll talk to you later." That was messed up because he was always sure to text or call when he needed help with his college course math homework, and I even helped him clean his old apartment and the new one he recently moved into. He even said "don't text me or call me anymore." That hurt. I feel embarrassed and bad since I embarrassed him. I also feel used. I was just caring about if he was okay, but apparently that's a bad thing. I never thought he'd break up with me over something like this. Idk what to do, I'm very sad and I kinda feel depressed myself. Is it a bad thing to care about someone??