Hi OP - I’m a doctor and a close relative has similarly been discharged from hospital after recovering from CV. I struggled to find any info apart from the Government “self-isolate for 7 days from when symptoms started”. It wasn’t clear to me whether this ALSO applied to severe/hospitalised cases, or whether they might be “more infectious”.
Spoke to my relative’s consultant today, who said I should abide by this rule for people discharged from hospital too - or at least there is no evidence to the contrary. This makes sense to me as a clinician too. My relative commenced symptoms approx 2.5 weeks ago, and he said it’s fine to enter house to care for relative without masks/2m distancing, but obviously observing usual hand washing/hygiene principles.
Relative has had no fever for a week and never has had a cough, to be fair - but yes, a cough alone which is not worsening is very typical for post any respiratory virus, and should not concern you.
Relative is usually self-caring but lives alone, is elderly and has been critically ill, therefore will need some support with food/washing from myself and other relatives for a few weeks, I anticipate.
Can I just add that could not be prouder of the NHS, who have cared for my family fantastically.