ur status has changed, so u need to apply/get visa.

I have also same situation and I am same phase....still confused...

This is what i found in Murthy.com
It might help you guys a lit bit.

Client: 
 I
am currently on H1B and going to transfer to F1 visa. just wanted to
know if my transfer gets approved from USCIS, is it necessary for me to
leave the country for stamping or I can still live on F1 status without
stamping. I would really appreciate if somebody could help me with this.

Attorney:  
you
do not need a valid visa to be in valid status in the U.S. In addition,
if you travel to Canada or Mexico, you may be eligible for automatic
visa revalidation so long as you had a valid nonimmigrant visa when you
initially entered the U.S., has maintained your status, was absent from
the U.S. for 30 days or less, has a valid passport, and is admissible
otherwise. In that case your visa would be extended and converted to
the new category for which you had your change-of-status application
approved. However, when you travel to other countries, you would still
need to apply for a new visa to re-enter the U.S.

Regards.

Still dint get the answer from the someone who actually did the way I needed.

I've seen 2 options though i'm not a lawyer, so do some more research.

Either u need to change your status from H1B to F1 here inside, or Leave US and come back fresh with new F1 visa (new I-20). The old one doesn't exists any more since it already got changed to H1B. You need to leave the country within 60 days. And make sure you will not be in the status next day you leave your job so got to be careful, and should talk to the employer about the scenario just to bridge the gap.

Regards.