If you want to get a good indication of your metabolic state yourself, try checking your basal temperature. This is a link to a good description of how to do it and what it can show. I've found it to be a good indicator myself, and if it shows low metabolism, then it will require follow-up lab testing to identify cause and determine medication.
http://www.drbobnd.com/low_thyroid.htm
By the way, if you use a digital thermometer, I'm told the best way is leave it turned off and insert in the armpit (per directions) for the full 10 minutes to get it fully stabilized, then you turn it on and and take reading.
Under eating is not a good idea. It actually causes you to keep weight on. The body thinks it is in famine and stores available energy in the fat cells. Do you know what your calorific needs are a day? For most women it is 2,000 calories. If you do not eat enough you will not lose weight especially if you are hypothyroid. I know it sounds weird but that it the fact of it!
Having only 3 periods a year is definitely a serious thing. It may not be hypothyroidsim but Cushing's Disease. You really do need to get some tests done! Beg, borrow, save up! But get those tests done.
With the activities you participate in, it might just be your muscles that are accounting for your weight. Muscle tissue is denser than fat tissue so you wouldn't necessarily LOOK fat to weigh what you do. Maybe you could try changing around your exercise a bit and see what happens.
If you don't feel well, you should see a doctor, particularly if you have other symptoms of hypothyroidism, as left untreated hypothyroidism CAN be very serious. Only the proper blood tests can tell for sure.
I think you mean hypo-thyroidism where your thyroid would be underfunctioning which could lead to weight gain etc. The only way to know for sure would be by getting a blood test, and you would have to see a Dr. for that.
To answer your question "is it serious?" It can be serious if you are extremely hypothyroid then it can put strain on your heart. If you are experiencing some of the other symptoms of hypothyroidism then it can effect your quality of life... i.e. fatique, malaise etc.
Only you know how you feel, if you are not feeling well, then you need to see a Doctor. If it is just a weight concern then your thyroid may or may not play a role.