This is actually possible. You can do something like this:
nohup sh -c "printf 'foo\nbar\n' | myScript.sh"
That will pass foo and bar as input.
But don't do that. Just don't use read. In fact, I can't even think of any good reason to ever use read inside a script. I'm sure there are some edge cases where it is necessary, but you should avoid it whenever possible. Having your users type in data is cumbersome, prone to errors, and makes automating your script impossible.
So just change your script to read the data from the command line:
#!/bin/sh
info1="$1"
info2="$2"
echo "$info1 $info2">>log.txt
Then, run your script with whatever you want as parameters:
myScript.sh foo bar
or
myScript.sh 'this one has spaces!' bar