a medical centre is different from a doctors office.
also doctors offices also have you do a urine sample BUT, if it is not coming up clearly to read pregnant or negative, they will do a blood test, which like i said is 100% accurate other than urine tests and pregnancy tests which can be false [sometimes] it wouldn't be too early, even on pregnancy test boxes, it said in print:
you can test 4 days before your period and get a result that early. Your fine to test and do this anytime.
You dont want your mom finding out, thats understandable, but would you rather put this off, and end up pregnant, or get it out in the open with your mom, say you think you could be pregnant and would like to go to the doctors to find out with a blood test.
i'd take getting it out in the open over waiting and stressing out about something like that. Pregnancy isnt something to put off and it will go away. id get it dealt with sooner.