So my story Her Light, Sessh travels back in time and runs into the younger version of himself.

How the heck can I write about them interacting without being confusing???

You could try using terms like "the young daiyoukai" and "the older daiyoukai", or "the younger Sesshoumaru" and "the older Sesshoumaru".

Maybe, if you show "young Sesshomaru" interacting with peers or servants who might be fond of him, you could have them refer to him with a cute, short version of his name, and you could adopt that in some of the passages that refer to him during this time period. If he's a stiff who does not allow such familiarity, maybe you could refer to him from time to time as "Prince Sesshomaru", and the older version as "Lord Sesshomaru".

I like those ideas.

Maybe you could give the younger version a nickname, and have the older Sesshomaru comment on how much he hates/hated that name.

Actually, I had to deal with something very, very similar in A Tangled Mess. What I did was this... the Sesshomaru that was the main one in the story I called Sesshomaru then refered to the other as the feudal version of Sesshomaru or something similar. That was until I had Kagome tagged him with a very disrespectful nickname. After that, when things smoothed out, it was a version of 'her' Sesshomaru and the feudal one. It seemed to work out quite well and no one ended up too confused about what I was doing. As their personalities were slightly different, it was easy to figure out which one was which even in conversations between the two Sesshomarus. If you want to look at what I did, it was in the last several chapters (I can't remember the numbers of them at this juncture, sorry), probably between 5-7 of them before the ending.

Hope that helps!