Not the writer of this information below.
I'm not the writer of this article.
Tail and fin rot can be prevented by keeping ammonia and nitrite levels low, adding salt at regular intervals, and quarantine of new fish. Guppies are particularly susceptible to this disease, and you will first recognize it as a ragged edge on the tail fin. Healthy adult tail fins should have a fairly straight edge, though sometimes adolescents will have temporary ragged fins due to uneven growth. As the disease progresses, the other fins become ragged, and the fins develop a white (sometimes though not always, fuzzy) margin. Sometimes, the fins will also develop red bloodspots. If the disease is allowed to continue, your guppies will die. In most species of fish this disease is a combination of bacteria and fungus on the fins themselves, however guppies tend towards acquiring an internal bacterial infection which spreads to the fins. You may try the salt treatment (instructions given later), as this sometimes does the trick. If that doesn't work, an antibiotic such as tetracycline can be used. Let your pet shop help you. They will specifically need to know if you use a bio-filter as many antibiotics will kill your filter.
http/healthybetta.com/articles/Illness%2...sis/finrot.html
Red spots on skin can be caused by:
Regarding the small red dot, small pinprick like haemorrhages (called petechiae) can be due to a local lesion, a generalised septicaemia or toxaemia caused by acute viral and bacterial infections.