Some info on tongues from a practicing Charismatic Catholic.
Scripture seems to indicate that there is more than one “variety” of tongues. There is public prophesy with interpretation as said in 1 Cor.; there is speaking in another earthly language, as was done by the disciples in Acts; and there is the “groanings of the Spirit” or private prayer in tongues as in Romans 8:26. It would seem to me (and to some others) that the first two would need interpreters, and the third one does not.
In 1 Cor 14:28 it says “But if there is no one to interpret, there should be silence in the assembly, each one speaking only to himself and to God”. This says two things - first, that just because there is no one interpreting for humans does not mean that the tongues do not exist. Second, this says silence “in the assembly”, as in, not speaking in tongues so that all can hear. Rather, one is indicated here to keep “silent” – to keep it to themselves rather than speaking publicly. This then ties into Romans 8:26 (groanings of the Spirit) and shows that one could have the gift of “silent” tongues, only between the individual and God.
The young woman at the abortion center that you metioned was spekaing in this third, more private kind of tongues, which is by FAR the most common use of the gift. Tongues is also considered to be one of the lesser gifts, not nearly as valuable as prophecy or teaching to the Community.
As for private speaking in tongues, this is the Holy Spirit which speaks through us to express things which are beyond words. For most of us Charismatics, it happens when the words of praise/prayer no longer suffice. It can either be in Earthly (“foreign”) languages (which can sometimes be understood by their native speakers), or in the languages of the angels. Both of these could be interpreted through the gift of interpretation of tongues. But it does not HAVE to be interpreted, as it is not for anyone else but me and God, and He already knows. As stated, this form of personal communication differs from the ones requiring interpretation.
And yes, sometimes it does sound like Aramaic.

Sometimes I have heard it sound distinctly like a real language that I might recognize, were I well educated enough. Sometimes I wonder if tongues are ever languages long since dead, from civilizations who left behind no record of their language, or from tribes deep in the jungles or the steppes somewhere. Sometimes it sounds to me like four or five syllables repeated in a pattern, as one might pray, “Jesus Jesus, have mercy on me” repeatedly.
Scott Hahn in his “Scripture Matters” explained that that revival of the gift of tongues could be a warning from God. It also happened in the Old Testament before some disaster struck, and also in the New, before the Romans invaded.
Hope this helps.