Would you get an STD test for a girl you just wanted to hook up with?

Even if she tested negative you can still get an STD. STDs are like punishment for living a sexual imoral life.

1 Corinthians 6:18

Flee from sexual immorality. Every other sin a person commits is outside the body, but the sexually immoral person sins against his own body.

Hebrews 13:4

Let marriage be held in honor among all, and let the marriage bed be undefiled, for God will judge the sexually immoral and adulterous.

1 Thessalonians 4:3-5

For this is the will of God, your sanctification: that you abstain from sexual immorality; that each one of you know how to control his own body in holiness and honor, not in the passion of lust like the Gentiles who do not know God;

Yeah - unless you take precautions and wear protection