Learn Finnish: Tulen juuri lääkärin luota. - I am just coming from the doctor's.

While lääkäriltä is perfectly understood, Finnish strongly prefers using the postposition system (luo, luona, luota) when talking about going to, being at, or coming from a person's place or presence. Since you are coming from the doctor's office, lääkärin luota is the most natural choice.

Why is lääkäri in the genitive form (lääkärin)?

The word luota is a postposition. In Finnish, almost all postpositions require the noun coming before them to be in the genitive case. This is why lääkäri changes to lääkärin.

How do the different direction forms for this postposition work?

Like many Finnish location words, this postposition has three directional forms. You use luota for coming from someone's place. If you were at the doctor's, you would use luona. If you were going to the doctor's, you would use luo or luokse.

Doesn't juuri mean root? Why is it used here?

Yes, as a noun juuri means a plant's root. However, it is also a very common adverb meaning just, exactly, or right now. In this sentence, tulen juuri means I am just coming or I just left.