A 2:37 isn't bad. How old are you?
If you can run 5 miles a day, then I think you have more than enough stamina for the 800. You should work on speed, and probably your form.
When you're running, what's your arm action like? If you're crossing over your body a lot, or not pumping your arms, then that will slow you down a lot.
Something I've tried which seems to help is sprinting downhill without slowing yourself down. This gets your body used to longer strides and moving faster.
Granted the 800 is more of a distance race than it is sprinting, improving you speed definitely wouldn't hurt.
I'm 16 but the other group of runners from other schools hit like a 2:20 I think I need more sprint work my form is fine
1200s are where it's at. They suck, but they help.