There's a limit to how dignified tests can be, unfortunately. There are 'test at home' kits for things like chlamydia where you dip a special stick of plastic in your pee and send it off. In many places, you can get them free at chemists if you're 26 or under. For HIV etc, you can be tested via a blood test (which will probably also be looked at for syphilis) after a month following the sex or (somewhat less accurately) via a mouth swab. Going to a sexual health clinic will get you the widest range of tests in a supportive and discreet environment. For all these, you typically get contacted by text message rather than anything indiscreet.
Different people have different ideas about numbers. For some, more than zero (or, if married, one) is too many, while others feel failures if they've had fewer than ten partners in a week. Their opinions don't matter. If you're happy, hooray. If you're not, use the experience to help you be happy in the future.