How to make my boyfriend feel safe and secure with me?

My boyfriend (19m) is a rather non expressive person, he has a super hard time expressing himself; he also does not open up easily. He doesn't like relying on people and doesn't like being vulnerable. However he did try a few times and I seem to have dismissed him completely? instance 1: he was having a bad sinus attack and he called me so i frantically started telling him how he should sleep, get off his phone and have some tea; he said he just wanted to distract himself from it but i made it worse. instance 2: he told me how he thinks he might have emotional blindness, and i asked him what that is and why he thinks that way, then i searched about it and i was like "SHUT UP YOU DONT HAVE THIS, THIS IS BS YOURE ALRIGHT", my intention here was to let him know that there's nothing wrong with him but it came across very badly. 2 days ago he told me mid-arguement (where he almost broke up w me) that he doesn't feel safe with me, he feels like he can't come to his own girlfriend with his problems. I think i should mention that he is someone who doesnt take things very seriously and im the opposite, so sometimes he'll just say smth as a joke but im too sensitive and i take it to heart. This, he says fucks with his mental peace.We're perfectly fine now but I really want to be able to become his peace and quiet and I want him to be able to trust that I can soothe all his worries.