Here's a breakdown of the sentence.
오늘도: again today; once again today (particle 도 is for again, too, as well, etc).
나밖에 업다고: simplification of 나밖에 없다라고, where 라고 is a quote suffix like "that".
* 나(me) + 밖에(except) + 없다 (there's none) + 라고 => that there is no one but me
말할 것만: 말할(say) + 것 (that) + 만(particle for "only") + 같아서 (it appears/seems)
=> (as it appears) you might say...; (anticipating/fearing) that you might say...
So it is:
"Because it appears you might say there is no one but me (for you) again today..."
Or,
"Anticipating (Fearing) that you might say you have no one but me yet again today...".
"만", which is untranslated, suggests a negative sense here, but it's not clear.
It is an adverbial clause expecting to be followed by a main clause, but often the main clause is left unsaid, especially in poetic languages.