The best way to well understand the usage of the French verb "fatiguer" is perhaps to refer to some examples shown in the following forum discussion, as given below:
forum.wordreference.com/showthread.php?t=393442
In particular, for the case given in your question, it should be "je suis fatigué(e)", where the word fatigué(e) is transformed as a past participle, an adjective. (The additional "e" given in bracket is for feminine speakers in this sense.)