This is really long. I apologize in advance but I'm trying to be as detailed as possible. Here goes...I coach field events and work a lot with weight training. From my own experience, there are several things you should focus on:
The first is strength training. But don't just go into the weightroom and do the one set to failure type workouts. High Jump is a dynamic event so you should prepare by doing several types of exercises twice a week.
1-Deadlift, cleans, pulls, presses (for your arms) and squats. Focus on these types of exercises because they'll develop the explosive power you need to jump. I can't stress proper lifting technique enough, though. You should ask a coach at the school to guide you through them. If you don't have a competent coach, ask the trainer at your local gym. A lot of times, they'll be happy to help you out. As far as a lifting program, start out with something like this. 3-4 sets, with increasing weight and decreasing reps as you go. Something like 6 reps at 55% of max, 4 reps at 75%, 3-4 reps at 80% and 2 reps at 90%. Gradually increase your maximum lift (I.E. 200 lbs to 220 to 245, much like you would increase mileage over several weeks) Two other days, take a deck of cards and do pushups and situps with it. Flip a card over and the # on the card is the reps in your set. Face cards are 10, aces are 15. Do it until you're too tired or you finish the deck (whichever comes first). This will help build your general strength.
2-Do a lot of Core/Midsection stuff. Strong Midsection is IMPORTANT to any athletic activity. High Jump is no exception. Medicine Ball, weighted crunches, and good mornings, stuff like that. Incorporate this into your weight lifting so it's done before or after the explosive lifting.
3-Do some conditioning to build general athleticism. This is overlooked all too often but it's probably the most important thing you can do for yourself at a young age. I coach college athletes but we have very limited facilities. Often, we'll play 1/2 court basketball and everytime someone scores, everyone runs to half court, slaps the line and runs back and continues the game. We also run suicides on the basketball court and do a lot of plyos. Hop up stairs (Never Down) or jump back and forth over a cone. Also, stand with one leg to each side of a cone and jump in the air, turn 180 degrees and land facing the opposite way. Work up to 360...it's tougher than you think. Lastly, to work on your vertical, take a piece of tape in your hand, jump up and slap it on the wall. Land and jump up immediately and try to get higher than the tape. Do this for 30-45 seconds and 2-3 sets. It's a great workout that can be done anywhere.
If you made it through this, I hope it helps. Good luck with your training and your upcoming season!