I (f) am afraid that I peed myself during sex?

Don't worry, you probably didn't pee yourself, but "squirted". In other words, you experienced female ejaculation. This is normal and also common. Arousal during sex and the stimulation of the G-zone produces a watery fluid in the Skene's glands of a woman, which flows out through the urethra. This «ejaculation» has nothing to do with sperm. When you are aroused, the G-spot gets more blood flow and swells slightly. For some this triggers an orgasm, for others it actually gets the juices flowing. Orgasm and female ejaculation are not necessarily connected.

Is this liquid urine?

No. Even though this fluid comes from the urethra, it is not urine but glandular fluid. This can feel like having to pee because of the proximity of the G-zone and Skene's glands to the urethra. However, it is a liquid that only fills about a teaspoon.

Is it embarrassing if I ejaculate as a woman?

Not at all! On the contrary, in many cultures this is celebrated and many partners even take it as a compliment for their skills as a lover.

Did she fake the orgasm if she didn't ejaculate?

No, orgasm and female ejaculation are not necessarily connected. They are two different processes. Female ejaculation is not a sign that the woman has climaxed. Nor should it be set as a goal to prove that the sex was particularly good. Many women do not experience female ejaculation in their entire lives.

Is sperm disgusting?

No, sperm is not disgusting. Sperm is something natural and is just as much a part of sex as any other bodily fluid. However, it is your right to communicate whether you like contact with semen or not. No one should do something they don't like. Some people like to touch/swallow semen, others don't. As always, the same applies here: be honest. Definitely don't swallow if you don't want to, and definitely don't cum on someone without first getting explicit permission to do so.