The BMI charts don't judge whether or not you have an eating disorder. Nor do I think they take into account the differing body types humans have. They are a "one-size fits all" approach to what is considered an "ideal" weight for people.
That said, you do have a very low BMI. It's 16.3. That is enough to raise concern, just as my very high BMI is enough to raise concern. A "healthy" or "ideal" BMI is considered to be between 20 and 24. At 5'7", you would need to weigh about 129 to hit 20.
There is no doubt that being too thin can cause ammennorhea, which is the lack of a period. However, going off birth control can also screw with your cycles, so four months might be a bit soon to declare it true ammennorhea.
I am guessing that being in the Air Force, you probably have lived an extremely athletic lifestyle, which can also result in not getting periods. Many elite athletes don't get periods. If you do exercise a great deal, cutting back on the workouts may help to get your cycles more regulated, too.
As for whether or not you have an eating disorder, I can't answer that. None of us here can. However, I am somewhat concerned that at the very least, you may have a disordered pattern of eating.
105 pounds is definitely quite thin for your height. You may be very small boned and naturally petite, which certainly does happen. However, I would consider trying to make eating regular meals a more focused goal, rather than gaining weight. You don't necessarily need to eat copious amounts of food, but consider that when you do get pregnant, you will want to ensure your child is getting all of the necessary nutrients from you. Make eating breakfast, lunch and dinner a priority, and take it from there. It is absolutely essential that you eat enough to fuel your body during pregnancy, and getting your body prepared for that major change is critical.
If you haven't already started, take a prenatal vitamin daily. Make sure it contains 800 mcg of folic acid, as that is critical to fetal development, and it's good for us anyway. You can make your meals as healthy as you want. Eat whole grains like oatmeal with dried fruit for breakfast. Make it with milk instead of water to gain some protien and dairy. Incorporate nuts into your diet, as they are full of the healthy fats we all want to get more of.
The bottom line is this... if you find the idea of eating three meals a day scary or worrisome because you may gain weight, then you should find a therapist and talk about a possible eating disorder. If you find the idea time consuming, but you're willing to do it, then you probably have just become overwhelmed with life and haven't been taking care of yourself properly.
I recommend buying the book "Intuitive Eating." If you truly are anorexic, IE is something that can be challenging early on in recovery, but if you've just become adjusted to eating in a disordered way, this book can really help.
The bottom line, however, is simple. If you want to get pregnant, you need to eat more. Not because I necessarily am convinced your ovulation issues are related to your weight, but because at such a low weight with such an erratic eating pattern, you would be risking the health of your baby if you could conceive right now. Furthermore, consider that when pregnant, you should gain about 20 to 25 pounds, especially because you are starting at a very low weight. If that idea is very difficult for you, then I would definitely say it's time to be assessed by a professional to see if there is reason to support an eating disorder. If there is, you want to get that under control before getting pregnant.
Good luck. I have dealt with infertility, and it is very, very hard. I wish you all the best and hope that by eating more regularly, and perhaps exercising less (if you do exercise an extreme amount currently), you will be able to easily get pregnant and have that beautiful, healthy baby you dream of...