Why? While sometime we would treat for a condition without getting the final, definite diganosis - since the potential benefit outweighs any risk that can be caused by the treatment. And symptoms of Chlamydia can be similiar to several other infections and each requires different treatment so I still out suggest getting tested to determine the appropriate treatment.
Why the risk. Chlamydia is a significant germ that deserves proper detection for both the individual and anyone that person has had sex with. A person can have it without symptoms for years, pass it on to others and cause infertility in sexual contacts. If you worry that you have it, find out, get treated and tell your partner.