"Day after day" describes situations that are always the same old, same old, without changing. If there is change, you may say: "Day by day, my English improves." That means your English is getting better gradually, little by little.

If the situation lasts for a long time, use "day in, day out": "She cooked and cleaned day in, day out for forty years" (Longman Dictionary of Contemporary English).

If something happens continuously and all the time, use day and night: "He was attended by nurses night and day" (Longman). Here, "night" is put first only because the nurses' jobs at night are considered more wearisome to perform than during daytime.

In this Jazz oldie (Night and Day sung by Billie Holiday) that I'm listening to, the night is long and lonely for Lady Day:

... Night and day you are the one

Only you beneath the moon and sun

Whether near me or far

It's no matter, darling, where you are

I think of you

Night and day

Day and night...

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