Problem Formatting and Sorting Dates

First time posting, so I hope I'm doing this right.

I work in healthcare and use Excel 2013 on my work computer. I frequently have to download spreadsheets of data that come with dates in "General" format which makes it sort A to Z rather than oldest to newest. If I select the cells and change format to "Short Date" it appears to change the format but still doesn't function correctly with sorting and the data stays aligned to the left instead of the right of the cell. If I click in the cell as if to edit text and then press the enter key it solves the issue, but this method is time consuming with larger data sets. I keep thinking there must be an easier way to fix the issue but I have yet to find one. Any help would be appreciated!