Hi there!
You are only eligible for the JR Pass if you enter Japan with a Tourist Visa, (aka "Temporary Vistor entry status"). This status has a maximum duration of 90 days / 3 months, so as you'll be in Japan for 4 months, I think it's likely you won't be in the country with the visa/status needed to use the Japan Rail Pass I'm afraid :(. You should check with your school however on this to get confirmation on how they expect you to handle entry status in to the country. JR is very strict on this I'm afraid...
For reference, you can activate your JR Pass anytime up to 3 months from the date of purchase, and on activation can specify a starting date for the validity period anytime within the next 1 month. For example, if you ordered a JR Pass today, the very latest you could activate it in Japan would be 13th Feb, at which point you could specify a starting date for your validity period to be any day until the 13th of March. Because of this flexibility, you do not need to start using it as soon as you arrive.
Hope this helps!