I go to Chabad but don't observe every Minhag. I'm 13 and wear a Tallis Gadol to begin with but when I tried putting it over my head I felt so connected to Hashem and I concentrated better. But would people look at me funny if I did this in a minyan? Is it halachically permitted?
The Mishna Brurah 8:4 writes at the end:
משמע בגמרא שבחור לא היה מכסה ראשו בטלית אפילו הוא ת"ח
Loose translation : it seems from the gemara that an unmarried person shouldn't cover their head with a tallis even if they are a great Torah Scholar.
This seems to be the overwhelming custom of Ashkenazim.
For Sefardim it seems that it is encouraged to do so even if one is unmarried(Torah Scholar ) per the Kaf Hachaim 8:12:
עוד כתב המגן אברהם שם, משמע בקידושין כט ב שבחור שלא נשא אשה לא היה מכסה ראשו בטלית, אפילו הוא תלמיד חכם, עד כאן. אמנם הרמב"ם בסוף פרק ג מהלכות ציצית והא"ח דף ד' עמוד א' והכלבו סימן כ"ב דף ט"ו עמוד ג' כתבו כי גנאי גדול הוא לתלמיד חכם שיתפלל בלא עיטוף ראשו בטלית...
It seems from the Rambam that it is disgraceful for a Talmud chacham to daven without covering their head withat a tallis.
See the Kaf Hachaim which quotes many more sources on this issue.
Its halachically permitted. There are minhagim against doing this for Ashkenazim, but the halacha is not on their side for this practice. A similar situation would be sleeping in the sukkah. Everyone is halachically mandated to sleep in the sukkah, but the main minhag in Ashkenaz was not to sleep in it. And so while they have now found halachic justifications to support their minhag, it is still a valid halachic decision to sleep in a sukkah. Same for the tallit. People might look at you funny, but you would have many sources to rely.