Yes. If you want to say that she was able to get get hold of you use "hun fik fat i mig" (you tried to run away, she was looking for you, she tried calling you)
If she was standing next to you and grabed you use (tog fat i mig)
It sounds a bit like the Dutch "Ze hield mij vast". ("Hun fik mig fat" ?) The Dutch 'vast' is related to the 'Fasten' in "Fasten your seatbelts".
I'd say 'got hold of', if 'reach' is used it implies her arm was long enough ... which is of course perfectly okay.
For your reference: the verb here is "at få", "to get". So the present, "She catches/gets a hold of me" would be "Hun får fat i mig".
what about "She got hold of me"? "She caught hold of me"? Both should be correct but one isn't.