"So I guess my question is, did this really happen? Does it go that deep?"
Yes. For me, anyway. All the blessed time...
Meditation is a great tool as an empath, in terms of knowing yourself and your own state v that of someone else. Discerning between the two is hard at first, and it may take some time to feel comfortable owning the 'realness' of these experiences (that will hopefully be lighter than that one).
Probably other tools like learning how to detach from others' intense energies, how to 'wash' the energies out of you, decording, etc etc will be necessary. Shielding seems to be a matter of personal taste, but you can use a meditative state to set some intentions around your personal boundaries and if you are a visualiser, also that might be nice to try for a while, different styles etc, to see how it helps you, or not.
A strong experience like that is certainly an eye-opener.