Pregnancy is a significant process which drastically affects your life during those nine months as well as for the rest of your life. As such, there are many "checks" that are duplicated to ensure we have the most possible information. If you have any concerns, questions, or thought you may be pregnant or wish to become pregnant -- please see your primary care doctor
To answer your question -- YES -- your pregnancy test should be done with a doctor. But to your second question -- YES -- a home pregnancy test is also adequate. In general, the home pregnancy tests, which use the level of HCG (a pregnancy hormone). While this test is not perfect (it doesn't turn positive till a few weeks after conception), it is fairly good for most brands in detecting pregnancy. Now, if you are positive, you should go to the pregnancy clinic -- because this should be confirmed. Confirmation can be done with a physical exam as well as the blood level of the HCG hormone. The other major reason is that there is many other testing and counseling that is required for a pregnant women. The clinic's test is more reliable, but the other tests required to ensure you and your baby are healthy are the real reason to go to a clinic.