Until you have a clear diagnosis and a strong understanding of the TCM patterns and treatment methodologies you probably shouldn't be treating yourself. Self treatment is not a good idea for many reasons - the main one being that it is somewhat hard to critically diagnose yourself. Advanced practitioners who have a good understanding of their body can probably treat themselves without harm, but it is still not recommended for all but the most general cases or acute situations where treatments from another colleague is not possible.
There are generally no prohibitions against certain points during menstruation or otherwise if they are being properly applied. LI 4, along with other points as appropriate, is often used during menstruation to smooth the menstrual cycle in cases where it is appropriate based on the diagnosis - so the point itself should not worry you. As for needling yourself, it is somewhat difficult to have good needling technique on yourself - again, one of many reasons to not treat yourself. This will improve with experience, however. When you hesitate with needling it is generally uncomfortable for whomever you are treating - in this case yourself. If you are clear in what you are trying to accomplish with the points and in your goal of helping your condition, the needling will be smooth.
As a student, having treatments from other professionals is a fantastic learning experience that you should not skip over. Furthermore, you should study and learn from the practitioner who actually helps you with your issues. TMJ is very treatable with acupuncture. This experience will be critical for your understanding overall but also for your trust in the medicine.