A "complete miscarriage" is when the uterus is emptied of all "products of conception" (nice term...). "Missed miscarriage", by contrast, is when the foetus has died or not developed, but there has been no bleeding. "Partial miscarriage" is when there has been bleeding, or a procedure, but there are "retained products of conception (RPOC)".
My notes, for example, say "probable expected miscarriage at 7 weeks", "missed miscarriage at 10 weeks", "partial miscarriage - RPOC after D&C at 12 weeks", "partial miscarriage - RPOC after D&C at 14 weeks" and "complete miscarriage at 16 weeks" - but I didn't have 5 miscarriages, that was all for the same pregnancy. The terms refer to the different stages of m/c.
So the "complete miscarriage" term on your file means that the woman you saw was satisfied that at the time she saw you, there was no remaining evidence of pregnancy. (This is really important for reasons of infection - if there was anything left, they would want to monitor it carefully, and possibly remove it medically/surgically, to avoid any risk to your health).
When the bleeding stopped is irrelevant - by the time I stop bleeding from my period each month, I'm usually 5 days after my period is due!
It's when it starts that counts for dating purposes. If you had completely finished bleeding within a week of your expected period date, that makes it sound even more likely it was a chemical pregnancy. The fact you had a positive pregnancy test for just five hours reinforces that. Implantation isn't an instant process - it takes place over a number of days as the blastocyst burrows deeper into the uterine wall and attaches itself more and more securely. HCG is produced almost as soon as it starts to implant - but takes a few hours to get into the urine. For whatever reason, the attachment process just didn't work properly the first time you get pg - which is extremely common.
A chemical pregnancy doesn't have to be before a period is due, it's just that it's far more likely that they will be picked up by someone testing early! Obviously, the longer you wait after your period is due but fails to turn up, the more likely it is to be a viable +. When I had a chem pg, I got +HPTs the day my period was due, and the following two days, before it went negative and my period turned up 3 days late. I then had 5 days of bleeding that was heavier than usual, with dark clots. Both the gynaecologists I saw, as well as my GP, said that they usually considered any pregnancy that lasted less than a week (approx time for completion of implantation) to be a chemical pregnancy rather than a clinical miscarriage, and to have little or no effect on future pregnancy chances. Certainly it seems that most research articles consider clinical pregnancies to be ones of over 7 days' duration, independently verified through blood tests/urine tests by a doctor or through u/s.
Basically, the effect of it is emotional rather than physical - even for 5 hours, you'd have had your hopes built up and then shattered - but if you consider that if you had not done the lunchtime test, only the evening one, you'd never even have known you were pregnant, then that should reassure you that your current pregnancy shouldn't be affected in any way by your past experience. Your head knows, your body doesn't! I read some research a while back which suggests that the average woman, not trying to conceive, but not using contraception, might normally experience 4 chemical pregnancies in a year without being aware of it - the only outward sign is that she might think her period was a couple of days late. I thought I'd posted an excerpt on here somewhere (it's on a password-protected academic database so I couldn't link to it), but if not, I'll try to find it again. If you're working in a biological research area and have an ATHENS password, you could do a search yourself through JSTOR or ProjectMuse - I think it was on the Cambridge Journals site.
I know it's hugely disappointing to have such a short-lived pregnancy, but you should view that as a very reassuring sign that everything's working normally. The fact that you're pregnant again so quickly should reinforce that. It took me another 8 months to get pg after my chem, and even then it turned into a complicated miscarriage! Personally, I don't have any residual fears from the chem - I can cope with that because it's statistically normal. I have more of a problem with overcoming fears of another missed m/c, and only finding out on a scan... As for pregnancy symptoms, it's quite usual to get a few very early, at 4 or maybe 5 weeks, as the progesterone rise kicks in, and then for the symptoms to subside as the body adjusts. Often morning sickness doesn't really kick in till about 7 weeks, even if you feel nauseous around the time your period would have been due. With my last pg, ironically I didn't feel nauseous at all till almost 8 weeks - by which time we'd already been told the pregnancy was likely to be non-viable. From that point until about 13 weeks, I felt quite sick. So I'm not paying too much attention to early symptoms coming and going!