How do I stop being so obsessed and attached to my boyfriend?

My boyfriend and I have only been dating for 9 months and I’m unhealthily obsessed and attached to him. I feel like it’s putting too much pressure on him and mentally for me. I feel sad if he isn’t with me all the time. We live in a graduate house with 6 other people and he says all the time it’s okay if we don’t hangout alone or don’t see each other one day. I understand I need to give him time and space but it makes me feel loved when he spends time with me and sees just me. I understand we have to include the whole house most of the time but sometimes I want our alone time and I get sad if i don’t get it how i imagine it. We do other things like have jobs, different times we come home, extra things like the gym and seeing family and friends so we do have time apart, but it’s the anxiety in me that thinks if i don’t see him he’s cheating or doesn’t love me anymore or something dumb like that. I know it’s not true but my anxiety gets the best of my thoughts. I’ve talked to him about this too so he’s aware and tries to compromise. I guess it’s just me. I need to rewire my brain to stop being so attached and obsessed. How can I do that? I don’t want to ruin this relationship I really really care about him.