The character can be based on a real person or well-known literary or mythological character, or created along common character tropes. Common character ideas include: robots, astronauts, literal statues (e.g. "The Thinker"), and mimes. For ideas or inspiration, look through pictures of living statues online, or go to an area of a nearby city in which living statues frequently perform. Start by visiting costume stores or novelty shops to find the necessary wigs and clothing for your costume. If you'd like to custom make your own costume, you can visit a fabric store to purchase an appropriate color and style of fabric, and then sew your own costume. If you have the option, choose a cotton fabric for your costume. Cotton holds its color well, even if you're performing in rain or snow. To flesh out your appearance as a human statue, you can accessorize with objects to wear and hold. Look for objects that match your overall theme: if you're a robot, hold an imitation computer; if you're a statue, hold a book to "read"; if you're a pirate, hold a plastic sword and hook. Sometimes just going shopping will be enough to inspire the costume, character, and actions you choose to perform. Yard sales, thrift shops and antique shops are best. You're bound to find something odd that will spark your inspiration. Other helpful places for props are home improvement stores (if you're looking for mechanical items) and fabric and craft stores. Items found at these types of stores may spark your creativity and give you ideas of how to accessorize your statue character. Many living statues cover themselves completely in makeup, to give them the appearance of being a statue, robot, or other non-human character. Depending on your natural skin tone, white makeup works best; copper and silver are other popular face-paint colors. You should be able to find costume makeup at a costume or hobby store, or through most online retailers. If using a white or non-metallic color, use water based cake-makeup as opposed to oil based. If you use oil, dust it with a finishing powder so it doesn't smudge. In order to draw attention to your eyes, you may want to line them in brown or black with regular eyeliner. Adding extra makeup (like lipstick or blush) on top of your solid base may be necessary, but keep it minimal unless the makeup is an essential part of your costume.
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One-sentence summary -- Develop a character. Make a costume. Accessorize your character. Apply makeup to flesh out your character.

You might be tempted to cope with your panic episodes through self-medication with drugs or alcohol. This is always a bad idea. For one thing, it fails to address the underlying problem. You are merely masking it by temporarily altering your brain chemistry and putting yourself at risk for alcoholism, drug dependency, and a host of other health problems. For another thing, it is counter-productive. Once the sedating effects of the drugs or alcohol wear off, the panic often comes back more strongly because you have lowered your defenses. There are safe medications that you can use to temporarily control or reduce symptoms of panic disorder. This will not "cure" the problem or resolve it entirely, but it may prove helpful. Talk to your doctor about this option. Most often, meds will work best when paired with other treatments like therapy and changes to lifestyle that get at the root causes. One possible option is to take a serotonin reuptake inhibitor antidepressant, like fluoxetine (Prozac), paroxetine (Paxil, Pexeva), or sertraline (Zoloft). These work by changing the levels of the hormone serotonin in your brain, boosting your mood, relieving mild to severe depression, and decreasing the frequency of panic attacks. Antidepressants are generally safe and cause fewer side effects than other types of antidepressants. Keep in mind that antidepressants can take several weeks before they begin to work properly. You have to take them continuously, not just during an isolated attack. Benzodiazepines are central nervous system depressants that are useful in treating anxiety, insomnia, seizures, and other problems. Generally they act quickly, usually within 30 minutes to an hour, and give rapid relief of symptoms of anxiety or panic. Benzos are habit-forming when taken long-term or in high dosages. You can develop a serious physical or psychological dependence on them and experience withdrawal symptoms. They should usually only be used for a short period.
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One-sentence summary --
Don't self-medicate. Talk to your doctor. Ask your physician about antidepressants. Ask your doctor about benzodiazepine.