Hello! Does anyone know how I might make an outline of an illustration I made with the pen tool in Illustrator? The sort of outline I'm trying to get is one that just goes around the outside like in this jpeg but have had no luck yet
You have open paths. Making an union is useless. Try the following:
A not so exact copy of your drawing
Gaps are filled with red line segments
A differently colored rectangle is placed below the drawing
All is selected, the outside of the drawing area inside the rectangle is filled with the shape builder. After making the selection and clicking the shape builder, orange fill color was selected. Then the green outside was clicked.
The orange part has been taken aside. It's a compound path.
The compound path is released, the rectangle is deleted, the result is probably what you want. Remove the fill color and insert a stroke as you like.
It's possible that all gaps need not to be filled. Double clicking the shape builder tool icon you get a dialog for tool settings. You have a possiblity to detect some gaps automatically.