Congratulations for diving and designing your own training using the book. Not too many 16 year olds would have the gumption to do this.
FIRST: You probably are not aerobically deficient in the same way as an adult with a high HR at low intensities.
Here’s some explanation:
Let me begin by saying some things about training for young people. I have coached many junior (<20 years) cross country skiers so I have considerable experience working with people your age. Your physiology is quite different than an adult and as such the training for juniors needs to be adjusted. You are still at least 10 years from reaching the age where your aerobic capacity can potentially be maximized. Your heart is still growing as is the rest of your body.
Your heart is relatively small now compared to what it will grow to over the next years. It has to beat faster to supply the muscles with adequate oxygen. So kids HRs can seem crazy high to people not used to them. I often have seen young skiers who achieve HR in excess of 210 b/min. Even during easy training they will be at 180. After a few years of effective training their HR for the same efforts drop by 20 beats as their hearts be come bigger and stronger (able to pump more blood).
At your age and since you are just starting out I would forget the HR monitor and try to get as much sustained aerobic work done as you can. Regardless of HR. In fact those high HRs are the best stimulus for your heart muscle to become stronger. Your 10,000 steps a day at school are a good thing......... But, intermittent, short (like a few minutes at a time) low intensity exercise like walking between classes is not an effective stimulus for you to count as developing aerobic capacity. Ninety minutes a week will barely move the needle. Young competitive athletes by the age of 16 in aerobic sports like running, swimming, cycling and XC skiing typically spend between 8-12 hours a week training aerobically. Some of the is low intensity but much of it turns out to be fairly high intensity in terms of HR, due to the factors mentioned above. This higher intensity does not hurt their aerobic development long term unless high intensity is done to extremes. Since you are just starting out I'd suggest starting with 3-4 hours/week of sustained (more than 20minutes at a time) of aerobic work.
You have not said what kind of climbing you are interested in but I recommend you use these young years to develop technical skills. This is the normal approach for training juniors in many endurance sports: skills and speed first when you can develop them quickly and aerobic development a few years later when your body is done growing so much. Your body will never be as able to learn new skills quickly and easily as it is in the years between 12 and 20. So, this is time to work on developing them.
This is also a good time for you to be working at developing good strength. I don't mean like a body builder and trying to get big muscles but your muscles and nervous system are primed to develop with whatever sort of stimulus you give them. If hard technical or rock climbing is your goal then you can go to a climbing gym where you will develop strength and technique in one workout.
I hope this helps.