it could be the old blood implantation yes dont worry
Implantation bleeding for a start is quite rare, and would be more brown in colour and only really likely to last for about a day. Also it is unlikely that you would get this the week after your period ending...that would mean that you conceived during your period, which again is pretty rare. Could be that you ovulate early and that is causing the spotting...it does in quite a lot of women. Was your last period normal? I would maybe go get checked out at the docs if the spotting continues etc. Could be an infection or something causing the spotting.