Yes, you can be stressed out and not know it. For example, if you are a workaholic and cope with adversity by working longer hours, then you may become stressed out, as you ignore all the physical symptoms of stress on your body. Some people may also choose to not acknowledge their stress load, and choose to ignore the stressors and continue as if they are invincible and not susceptible to the effects of stress.
When you are stressed, your body reacts by activating the fight or flight response. This adrenaline response then induces multiple physical symptoms, such as increased heart rate, increased blood pressure, shortness of breath, tingling and numbing sensations, lump in the throat, butterflies in the stomach, muscle tension, headaches, nausea and vomiting, tremors, sweating, tunnel vision, and hypervigilance.
But you ignore your stressors at your own peril. If you continue to not address your stress, then your body will rebel and you will become stressed out or burnt out, as the fight or flight response was only meant to be activated short term to deal with an imminent danger, and was not designed for chronic activation, as is seen in stress and anxiety (which activates the fight or flight response long term). So if you become stressed out or burnt out, then you will experience additional symptoms of irritability, fatigue, poor concentration, disrupted sleep, poor appetite, anxiety, depression, negativity, loss of feeling pleasure, and social isolation.

If you don't seek help when you are stressed out, then you will eventually develop clinical anxiety or depression, and this will lead to significant impairment of your functioning, such as relationship problems, job/school problems, and problems with self-care.
So if you are stressed out, it is important to know the symptoms of being stressed out, so that you can seek help to prevent the development of an anxiety disorder or major depressive disorder.