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.
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.
Do you have any other symptoms like sweats, rapid heart rate, or do you feel anxious?
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.).
Here is a better picture:
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.