Help adv I feel terrible. I am applying for jobs, got an interview

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Help adv I feel terrible. I am applying for jobs, got an interview for a place I'd really like to work. Passed three roubds to get the final interview and did really well. This is where I screwed up though. HR had emailed me the night of my last interview stating they had chosen me as their final candidate and that I just need to pass administration in the company anymore, but I didnt notice the email. I usually check every day, but the next day was unusual: my grandparents were visiting for the whole day and I had a migraine in the evening. I had been previously contacted via phone call so I was waiting for a call, not expecting an email. Well... I answered the email after a day and a half but I'm worried it gave the wrong impression of not being interested in the position or of laziness of not checking my email. What should I do? Would it be ok to call HR and explain? I answered the email on Friday and havent gotten a reply since.