Can the word "subsubsection" be used in a thesis?
One very important point has yet to be touched on. Indeed, subsubsection is not a dictionary word -- and even if it were, it's awfully cumbersome. Saying "section 1.2.3" is neater and more informative, as it tells the reader exactly where to go.

The most important reason to use numbered references is if the order of your text changes. For example, if you move a particular subsection to another section or chapter, any references to it in the form of "the next subsection" will now be invalid. By using numbered references and attaching these to either the subsection header or a key sentence (as appropriate), the numbers will automatically update and your referencing will remain correct.

The above is applicable to references to anything.  It is very dangerous to write such things as "in the following...", "in the previous section we introduced...", etc. Such phrases do not refer to an exact place, and they can easily became invalid as you add, remove, or change parts of the text. Proof-reading will also be more difficult.