Is : Us and my grandmother went shopping correct use of a pronoun?
You can use this sentence structure test to see which pronoun should be used.
Start the sentence with just the pronoun 'us', leaving out "and my grandmother".
Us went shopping. (incorrect)
When you isolate the pronoun, you can easily see (or hear) that there is something wrong.
Remember that you need a subject pronoun to start a sentence.
Which personal pronouns can be the subject in a sentence?
I went We went
You went They went
"Us" cannot be used as the subject of a sentence, because it is actually an object pronoun. Which of the pronouns in this list can be used, instead, to indicate a group in which you are a member? Anytime you are talking about two or more people-- and you are one of those people--as a subject, you can use "we".
Now, there is the unusual phrasing . The other tutors answering have a good way to solve this:
We and Grandma went shopping. (Grammatically correct, but awkward structure)
Grandma went shopping with us. (Grammatically correct, clearer meaning, more natural sounding)
By using the preposition "with", you avoid using two names for the subject and instead add "us" in object pronoun form.