Is there a way to use cellpadding for just left and right? I am looking for answers but all I keep finding is CSS.
No, there is no clear way of doing with without position your <td> tag by using parent. Based on this: http://www.w3schools.com/tags/tag_td.asp there is nothing that is supported that will help.
I would suggest using attributes such as rowspan and colspan to help adjust table cells - using that will help you structure the content the way you want without having to use css.