sperm can actually live up to a week.
I know it's easier said than done but try not to stress a lot because then to much stress can lead to not coming out pregnant my midwife tells me this all the time.
If you ovulated on the 23, DTD on the 27th wouldn't have helped in getting pregnant, because the egg is only good for 12-24 hours. It is possible for the sperm on the 22nd to have met the egg, because sperm can live up to 6 days. My hubby and I got pregnant by DTD two days before ovulation. At this point you're 6dpo so testing would be too early. I got my first bfp 10 dpo, some women get it a day or so earlier, some later, all depends. Hope this helps, best of luck!