I'm looking for a way to make "heavy" oatmeal choco chip cookies. When baked, the cookie keeps the shape of the scoop instead of spreading out. Does using eggs or baking soda make cookies spread out?
One thing you definitely want to look for is recipes that include chilling the dough. Here's one, for example. http://www.tastebook.com/recipes/2692646-Thick-Chewy-Oatmeal-Cookies?full_recipe=true
The effect of chilling the dough is two-fold. First, because the dough will be cold when you put it in the oven the very outside of the cookie will become "baked", somewhat hardened and crystallized, giving the cookie its final shape even before the interior of the cookie is done, hence thicker cookie. This also illustrates another point. Be sure your baking sheet is cool, even cold. You might want to put it in the fridge between batches.
The second effect of chilling the dough is more about time than temperature. During the time the oatmeal chills, it is soaking up the liquid ingredients of your recipe. Less free liquid equals less spread.
Some keys to keeping cookies thick, beyond the chilled dough, are: use a starchier flour, use a fat with a high melting point, and use baking powder.
A starchier flour, like cake flour, will spread less than a flour that has higher protein, like all purpose. If you can't find cake flour, you could replace some of the flour in your recipe with a starch, like cornstarch or potato starch.
Shortening has a higher melting point than butter, replacing all or some of the butter in your recipe with shortening will allow the cookie to begin to set before the fat melts completely.
Finally, baking powder contains acids which help to keep the dough tighter. This helps it to "puff" more and spread less. If you can't use baking powder, you could add a bit of some other acidic ingredient to your dough (but cut the baking soda a bit as well or you might end up with cookies that are too cakey). A bit of a fruit vinegar, citrus juice, or cream of tartar would probably do the trick.
I think I understand your thinking, you want them to be thick so make the dough drier so that they don't spread out too much. In your case you've gone too far, adding too much flour or not enough moisture.
Cooking with oats is tricky because they absorb so much moisture, they do have a tendency to such moisture out if there isn't enough to rehydrate them. Try adding bit more butter, milk, or water (whatever the recipe calls for) until you get the right amounts. Also, you could soak the oats a bit before you mix them in to get them on their way so they don't absorb so much of the recipe moisture. The benefit of soaking them a bit is that you can tell sooner if you have the right consistency - if you add dry oats you need to let the mix sit for awhile so the oats hydrate, and only then will you tell if your consistency is right.
@Jolenealaska is right, if you want a thicker cookie then chill the dough it will help keep them from spreading too much before they crystallize.
Also, let the cookie sheets cool completely before putting more dough on them when batch baking, if your sheets are warm the first cookie dough balls you put on will start to spread out before you get the last ones on.