Your family and your Mentor while trying to be supportive are not being objective. That's not their job. They're motivated by their love for you. I don't love you. But I do care about people. And that's why I'm being honest with you.
I can assure you that you are not psychotic... Just young and immature. We all go through it. Lets not assign any blame in this situation or focus on who is right or who is wrong. But rather, let's focus on the fact that you feel guilty and the fear of that emotion causing you distress.
There's an easy fix for that... send her an email apologizing for your initial outburst and behavior and ask her to forgive you. Hell, you don't even have to mean it and you don't have to stay friends with her afterwards, but it will do wonders for your conscience.
Now let's address the probable reason why emotionally you put yourself in that position to begin with. At your age as with most people I'm sure you have feelings of insecurity or an inferiority complex as to your looks and your worth, etc. When someone has sex with you that's the ultimate acceptance by another person... or so we like to think. And when we have these feelings of inferiority and we get that acceptance we tend to guard it jealously.
It probably wouldn't have mattered if she had accepted your initial offer and had sex with him, it probably just would have taken longer for you to blow up at her as it festered over time... At least this way you got it all out in the open at once.
In your immature understanding of what sex is, in your case the need for acceptance, when this person had sex with your best friend who also gives you acceptance, afterwards you felt totally rejected by both of them. Even though I'm sure that was not their objective.
What you fail to understand is their motivation for having sex. Maybe they're just as immature emotionally as you are. Your friend probably experiences the same emotions feelings and fears as you. Probably has the same inferiority complex and the need for acceptance. Maybe even the guy does too, although he's probably just interested in dipping his wick.(ya, it's a guy thing, we can't help ourselves sometimes)
I'm sure you appreciate it when people cut you a little slack...why don't you cut them some too.
Now as for your thoughts of suicide, let me leave you with one last thought. Regardless of how you feel, any pain, or what problems you may be going through, your feelings, pain, and problems are temporary. Suicide is a permanent solution to a temporary problem. You should always stay in the game. Things do get better and they will get much better... Wouldn't it be a shame if you weren't around to experience it? You talked about how amazing the sex was... Wait until you experience it with someone you're in love with, who is in love with you and you both realize that this is the person you want it to last forever with... not just some **** buddy.