Young Writers Society

On the seventh day of the month July of the year 1937, my families life would never be the same.
Families should be family's since you're trying to show possesion, not making the world plural.

We hadn’t heard the radio announcement that day, that a large dust storm was coming our way.
I tried to do a little research after I read this, but I couldn't find much on dust storms themselves. Dust storms are known to be sudden. You may have done more research than I have on this though.

It was stupid of me, thinking a way not to stay at the school with my brother.
You need an of before a.

I told her, glancing out the window as I stirred the boiling soup.
This is entirely nitpicking, but soup simmers. I mean, technically, boiling would burn the soup on the bottom, but no one really cares. Just thought I'd point that out since you use boiling later on, which is fine, but you know, change up your vocab... Yeah...

It was about time that Will was getting out of school.
Do you mean Louie?

I had seen many dust storms, but this was just the beginning of storm.
There are a few inconsistancies within your story. From what I could find, dust storms do travel and can be monsterous. However, you say that this is the beginning of a storm. The meteorolgy (sorry for the sketching spelling) of the 30's was not what it is today, and duststorms are fairly unpredictable from what I understand. I don't know what you're going to do with these fact, but make sure your story is parallel.

Father and Rolly stood by mother, their foreheads creased with worry.
I would introduce Rolly as her big brother now rather than later.

Dust had gathered and laid themselves between the hairs of Father and Rolly‘s arms. Changing their skin color from white to dark brown.
Two things here. If you said dust particles, you could use themselves, but as it is, you could just get rid of themselves, and the sentence would sound better.
Where your first period is, that should be a comma. The second clause isn't a complete sentence.

My older brother coughed into his elbow as he waited for our parents to reply.
Very small nitpick. You cough into the crook of your elbow.

“She went to visit the Matthews earlier, she wasn’t to be home till late.”
Period where the comma is. Run-on.

I went to stir the boiling over soup.
This sounds odd. I like to give an example of what to do different, but I really don't know what to tell you.
If you stir soup that's boiling over, it will redistribute the heat, but it will only give you enough time to turn the heat down. I'm not sure what kind of appliances you would have in the 1930's. In the rural areas, it would have probably been a wood stove. I like the detail since it seems to be mirroring the chaos of the family. Maybe, both are so lost in thought and worried that it's almost a side note, and no one does anything.

It was early morning two days later when the dust storm ended.
I did a little research because a two day dust storm is hard to believe, but there was one that I could find. If you wanted to be really historcally acurate, it happened on May 9-11, 1934.

They came back hours later with Maria, with out Louie.
Without is one word.

I went about my chores. Checking the two chickens we had, to feed them. Only to find that that one had died during the storm.
The last two sentences are actually fragments. Replace the periods with commas.

I put the chicken on the chopping block and left it there, father would have to decide what to do with it.
Run-on

I’m not sure what I did, it’s all a blur to me.
Run-on