When you say "three days running," you imply that it is expected to continue in the coming days.

Two days running?

Hi!

If I want to say that something was happening, for example, on Tuesday, Wednesday and Thursday, i.e.3 days one after another, is it correct to say:

3 days running? does it sound natural?  It sounds perfect!
3 days one after another? does this sound better than the previous phrase?  Three days one after another is possible, but you will rarely encounter it. 

Here are two more natural variants:   Three days in a row.    Three days straight.

Thanks in advance!