I have a thin septum. Is it possible to make it thicker?

Hello! The septum can be made straighter and thicker as long as you are not going to damage your functional breathing. A thorough assessment is needed in order to explain what best approach could be adopted for your specific case. Straighter nose will improve the appearance of your nostrils which could also be adjusted. Again, you need to search for a specialist in septorhinoplasty surgery and make a fully informed consultation. 

Making the nasal septum thicker is possible and sometimes inevitable, but if you were to choose the ideal change it would be to keep the septum is close to its natural thickness as possible in order to maintain adequate space for breathing.From what you are describing the lower part of the septum is positioned slightly oblique on the anterior nasal spine which is often also asymmetric.Relocation of the caudal septum is possible and can be carried out through an open tip intervention or a closed approach.In the end, there are always some differences in the appearance of the nostrils, but they can be made less visible.

Hello
Thank you for taking the time to share your question
The best option for you is to find a surgeon that is board certified in both facial plastic surgery and otolaryngology in order to properly address your aesthetic and possibly functional needs. The enhancement you are looking for can potentially be addressed with a closed scarless Septorhinoplasty to adjust your septum at the base to improve the symmetry of your nostrils. In the hands of a properly experienced surgeon, this technique is beneficial because of the avoidance of a scar on the outside of the nose, much more rapid and comfortable recovery compared to an ‘open’ rhinoplasty, and less disruption of the nasal tissues. Additionally, if you have nasal breathing issues, you may be able to use your health insurance to offset a significant portion of the cost. 
Good luck!
Behrad Brad Aynehchi, MD