Has anyone fallen pregnant 4 days after their period?

I think I'm pregnant, we've only had unprotected sex once this month and it was 4 days after my period and I know you'll say of course you can, if you have sex you can.

But we were not in my fertile window so I assumed we'd be ok.

I've done a test and the line is so faint where as if it was 4 days after my last period which was a couple of weeks ago now, surely the hcg would show?

I feel really sick and my back is aching like crazy;

Experiences please

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