Honestly, you shouldn't have gone to a and e. It's only heightened your concerns and anxiety. Their tests are not at all sensitive. A small amount of spotting in early pregnancy is neither an accident nor an emergency.
You'll likely be too early to see anything on a scan either, which again will make your anxiety worse.
In the absence of bleeding at least as heavy as your period probably coupled with heavy cramps, it's likely that things are just fine. One sided excruciating pain (with or without bleeding) would also be a worry.
Even if it were a miscarriage, there is nothing that can be done. Sadly, they are all too common and the vast majority (especially when so early) require no medical intervention at all.
The earliest something is likely to be seen on a scan is 5-6 weeks, and even then, likely only transvaginally. You'd be highly unlikely to see anything like a heartbeat until AT LEAST 6 weeks, and in many cases, more like 7.
Early pregnancy is a worrying time for everyone, I get that. But it sounds like you're trying to medicalise something where there are no real indications that something is wrong. Normally, I'd be suggesting a wait and watch approach in situations like this...