Both “tomorrows” and “tomorrow’s” are English words. Each one has a different meaning so one would be correct in some sentences and the other would be correct in other sentences.
Please keep in mind a rule that I teach with regard to the apostrophe (inverted comma). NEVER use an apostrophe to form a plural!
So, NEVER write “tomorrow’s” when you mean “more than one tomorrow”. If you write “tomorrow’s” it is either a possessive that means “belongs to tomorrow” or a contraction of two words, either “tomorrow is” or “tomorrow has”. Here are some example sentences to help you understand:
“I promise that all of our tomorrows will be better than today.”
“When I ask her for the work, it is never ready. All I get from her is an endless stream of tomorrows”. (Her answer is always “tomorrow”.)
“Focus on today. Deal with tomorrow’s troubles tomorrow.”
“Today is fairly open. Tomorrow’s schedule is more crowded.”
“This is an easy day. Tomorrow’s the toughest day of the workshop.”
Tomorrows, this word is not used as much frequently but, yes it is used.
For example— If you save from today then the tomorrows belong to you.
So, here we can see that Tomorrows is signifying days to come in future.
Tomorrow’s, this word is used very frequently. And also one thing that tomorrow’s is actually ‘tomorrow is’
For example- The best preparation for tomorrow is (tomorrow’s) doing your best today.
So, here we already know that tomorrow’s (tomorrow is ) correct.
We can conclude that Tomorrows and tomorrow’s both the words used up are correct.
Hope it helps!