Should in the past [closed]

I should do it indicates that you have not done it.

So I should do it and I did it is semantically like saying I haven’t done it and I did it. It does not make sense.

I should have done it indicates that you did not do it.

So I should have done it and I did it is semantically like saying I did not do it and I did it. It does not make sense.

You need a verb that can inflect, like a “semi-modal” (I had to do it and I did it) or a non-modal (I needed to do it and I did it).

See also:

should
3. modal verb
If you say that something should have happened, you mean that it did not happen, but that you wish it had. If you say that something should not have happened, you mean that it did happen, but that you wish it had not.
_{Source: Collins — should}