It is possible to store the value in a variable using the back quotes or grave
accent(`) This is not single quote. You will find it on the same key as tilde
(~).

rt=`date+%b` ; echo $rt

Your second question, reading the month from the system, refering to the first
question, you know how to get the month from the system date. Use the command in
back quotes that will help you. The command modifies as below

grep -i `date command to extract month` /home/nerd/CALENDAR.TXT | sort