Your eyes don't look like they're bulging in that picture. Of course, it never hurts to get thyroid hormones tested, but I don't see anything indicative of a thyroid problem, by looking at your eyes.
Here is a better picture:
http://i.imgur.com/tTT9qVf.png
I get anxious sometimes, but only if I have to do a presentation in school or something. I don't randomly get anxious if that's what you mean. Last time I went to the doctor was back in april and all of my vitals were perfect (blood pressure, heart rate, etc.).
Do you have any other symptoms like sweats, rapid heart rate, or do you feel anxious?
I agree that it's really hard to tell whether or not your eye is bulging; it doesn't look like it to me... If I open my eyes really wide (which isn't what they normally look like), I can look hyper, as well. Would be much better to take a full face photo, with your eyes, like they normally are, rather than exaggerated, as in your photo.
It's a good idea to get thyroid levels tested, anyway.
Regardless of whether or not you have symptoms, you should get your thyroid blood levels tested. Here are the tests to request: Free T3, Free T4, TSH. This can be done as part of routine bloodwork, along with a CBC, vitamin tests such as D and B12, etc. Your eyes don't look like they're bulging to me, but it's hard to tell from the photo and it's a good idea to have these thyroid tests done routinely throughout one's life due to the high prevalence of thyroid disease, especially among women.