Hello.Very glad to answer for you."today"and "now" can appear at the same sentence .For example,It is 6:00now and today is a nice day.
Another example:Now that you don't love me ,I will leave here today.I would appreciate it if you choose my answer as the answer you want.I am alse very willing to answer your further questions.Thank you.It is very good to ask others when you have any questions.May you study even better.