Can you get pregnant without a penis or a sperm?

its very rare

Sperm + egg = embryo. Without either one, no embryo.

You don't need a penis but you do need sperm .

You can get pregnant without the immediate intervention of a penis thanks to modern assistive reproductive technology. A penis will be involved in the process at some point, though not in the same room as you.

You can't get pregnant without sperm.

One sperm is needed to make one egg of a human female pregnant. The usual method of getting lots and lots (millions) of sperms close to an egg is by having the erect penis jiggle around in the vagina of the female until the penis squirts semen containing all those sperms into the female. That is usually called "having sex".

There are other ways of getting semen into the vagina - it can happen if the male squirts outside the vagina, and then fingers covered in semen play in the vagina - not such a certain way of getting pregnant, but it has been known.

Did your school really not tell you much about such matters?