Am I being overprotective?

My boyfriend suffers from depression; we have been going out for 4 months but have been best friends for 5 years.

He has always had episodes but after a month into the relationship it has just become full blown... he has ED and I can understand it is embarrassing for him... he works as a deputy manager at a care home so he’s always stressed working 6 days out of the week, he feels like his manager doesn’t respect him and I can see how thats bringing him down.
He’s working through Christmas period (which he has done for the past 6 years). I have told him he needs to make a stand that he hasn’t spent Christmas with his loved ones since he was 17 but he refuses to do that.

I asked if one of the reasons he’s depressed is because of our relationship, he says he’s more depressed he can’t be the boyfriend I deserve as I am the only good thing in his life.

So I’ve started messaging one of his coworkers I used to go to college with, checking on him to see he’s okay at work.
Other day, I gave my number to his roommate after seeing the state my boyfriend was in (drained, not sleeping, sat on his bedroom in the dark not doing anything, talking about how he just feels trapped all the time), telling his roommate I was scared about my boyfriend and to message me if he starts to notice that he’s self harming or talks about killing himself.

I don’t want to be too overprotective and usually I wouldn’t be asking people to tell me how he is and what he is doing when I’m not around but in this case, I’m worried. He was there for me when my depression was bad and I really really care about him.

Am I being overprotective?
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