I recommend that you see your primary care doctor
or your OB GYN doctor about this issue. They should be able to give you some advice and also perform any testing that might be necessary.
The first thing that needs to be clarified is whether you mean that your period came three weeks ago or whether you mean three days ago. On the other hand, if you just had a bit of spotting of blood three days ago, that might not be a true period.
It is very important, whenever you engage in any kind of activity where there may be contact between sexual fluids and the genitals, to use protection. Even without intercourse or ejaculation, it is possible to become pregnant from these fluids if contact occurs.
Therefore, most likely, after confirming and clarifying that your period is indeed late, your doctor will probably want to start by checking a pregnancy test, which is a quick and simple test which can be performed with just a urine sample. If the pregnancy test is negative, then your doctor can perform more detailed questioning and examination to help figure out what might be the cause of your delayed menstrual cycle.