You are correct, "altrapar, " which means to catch, to capture, or to trap would be used in the case of catching someone falling or running to catch scattered coins. "Alcanzar" means to reach, to catch up with, or to catch (with the latter used in a sentence like "You cannot catch me in this race," or "You cannot catch up with me in this race."
Catch would relate to reach, not the past tense, "caught." Your example was future tense with a past tense verb. Also, I was a little surprised no one suggested the meaning "reached me by phone." One could say, "The nurse caught me at home to remind me of my appointment by calling me at seven a.m." Caught me or reached me would be interchangeable in that context, agreed?
To answer a few comments:
"Alcanzar" means catch only in the sense of "reach", and not in the sense of "grasp" or "capture". "She caught me" strongly suggests grasping or capturing and is thus incorrect (without a context such as "she caught me by phone", etc.)
"She caught me up" means "she imparted knowledge to me until I attained a current understanding", and in no way is this synonymous with "she caught up to me". In the former, I do the movement (physical or metaphorical); in the latter, she does.
It says ¨she caught me up" and ¨she reached me¨ are correct translations. This is confusing as these two sentences mean completely opposite things. ¨She caught me up¨ implies you were behind her whereas ¨she reached me¨ (another way of saying ¨she caught up to me¨) implies she was behind you. Which is it?
In Oregon (USA), you might hear someone say, "Thanks for catching me up," if a coworker were to fill them in on a meeting they missed. I think I've occasionally heard the past tense, though it's not as common.
I'm still interested to know if anyone is sure whether alcanzar can be used for reaching a person on the phone.