Heartbroken Kylie Jenner has spoken out for the first time since the sudden death of her hairstylist pal, Jesus Guerrero ... admitting the pain of losing him has been too much to handle.

In an emotional IG carousel posted Tuesday, Kylie called Guerrero her rock, always there to lift her up even on the toughest days -- adding in her heartfelt message that she couldn’t imagine how she would've gotten through the last decade without him by her side.

Kylie praised Jesus for his incredible talent and for his kind heart, and the lasting impact he had on her and so many others ... acknowledging her heartache came from a place of deep love.

She pined to hug him again ... and admitted she would do anything for one last deep convo with him.

It’s an unfathomable loss for Kylie, who had been prioritizing other matters before speaking out publicly.

Sources told TMZ that Kylie first learned of Jesus' death early Saturday morning. The next day, she spent time with his family, giving comfort and offering to cover the funeral costs and other expenses.