the 800 was my favourite event. without knowing you well enough, it is too hard to give you advice. I could only tell you what I did when younger and what I do now.
I say train year round. Do mostly the same training year round, just use different intensities at different times of the year. I think Lydiard didn't like young runners racing more than 1 race per meet but I would run 2 if I were in high school. 800 metres runners need more mileage than many think, in my opinion. Today I race from 400 metres to the 1/2 marathon and use the same training for all my distances. Saturday, I ran an 8 in 2:01.47 so we are about the same right now.
When I trained specifically for the 800 as my first event I trained generally like this.
Sunday--60 to 90 minutes slowly and easily. I would run on various surfaces and went barefoot for half the run on the softer surfaces (*I grew up running barefoot though just so you understand). I liked a rolling course to build strength. I'd walk 30 minutes.
Monday-- I took it easy. I'd ride a bike slowly for 30 minutes. I'd walk for 30-60 minutes. I lifted 2 sets of upper body weights and 1 set for lower. If I ran I'd go for about 30 minutes. I'd go through a thorough stretching program. I might swim 30 minutes. Overall, it took hours and was achieved in 2 practises.
Tuesday-- I'd run Speed Endurance on a Fartlek run or track. I used to do too little like 4-62 400s. Today, I run something longer for strength like 4-1000s @ 72 pace for 3:00 with only 200 metres jogs. Then I go right into 4- 400m in about 68s with 200m jogs. (The other day I ran 68,69,68,67). I don't want to go too fast here. My warmups and cool downs are long and this is where I include my barefoot running. Usually 20 mins easy jogging & then 10 mins more where I run 30 seconds striders with 90 secs jogs. Stretch how you need it. Massage yourself. I walk too. (* I walk everyday just so you understand).
Wednesday-- Like Monday. But also know that when I take a day off it will be on a Monday or Wednesday and I do it when I FEEL like it (about 1 time a week) but I always walk at least 1 hour.
Thursday-- So fun because it is Sprints. Can be fartlek or on track. On Fartlek I do 15-20 sprints by feel. They can be anywhere from 10 seconds to 40 seconds and the recovery jogs are run util a 2 minute segment is done. So s 20 seconds sprint will have a 100 seconds jog. If on a soft surface this is where I go barefoot. The warmup and cooldown for me is at least 20 minutes each.
Friday-- Like M & F.
Saturday-- I race or I time trial. If you are like me you will want to race or time trial at different distances. I treat my TT like races. I warmup etc. just like a race and I run different distances. I avoid doing them with others. See tomorrow I may run a 5K and then Saturday I'm running a rare 1200m. But for you I would probably keep the race distances down to what your high school runs because I'm thinking you may want to go to university as a runner.
Make sure you EAT WELL including breakfast. I eat about 2200 cals a day. I eat often, and my body never feels that it is starving. I take some vitamins. I'm careful about any medicines. Later, I have to get my sleep now. Yes, make sure you get the sleep you need. Good Luck!