Hi dear  Janet,
   Good day to you!For the sentence that you sent to me "I'm going grocery shopping tomorrow" is correct one ,coz we are not only use "will " and "be going to "... to express the future tense as a normal case  ,but also we can use the present continuous tense to express that sometimes  .For example:"i'm meeting my boss next sunday ." and  "i'm visiting my grandpa tomorrow "etc.:)

Cheers,
Zoe Chew
11-03-07