I've posted before about OOC/IC separation and the importance of it. That said, no matter what, I think we're all invested in our characters to one extent or another and sometimes, when bad things happen to them, it hurts.
It's perfectly natural to have a reaction like this and sometimes taking a break is so beneficial. Sindome is one of the few games I've played where I've had emotional reactions in real life, to the point I've had to AFK in scenes and mention OOC that I'm having a moment (i.e., bawling) and need to take a few minutes. Other times, I may play a little less, to get my head back in order.
Character death is up at the top of that and it's okay to feel a little depressed. For me, it's like binging my favorite show and finding it's over, and wondering what I'm supposed to do now. You'll heal and find a new character to love to iddy, biddy bits.
Take some time, really think on the new character you want to play and allow yourself to get excited for them. The blues will pass!