Unless you get over the fear, then you could let paranoia get the best of you, and go insane from it. It's one of those deadly infinite loops.
I've been fine with talking to myself in public (like mentioned in OP, I tone down or shut it when others are nearby or get close enough to give me odd glances). My main worry tends to be when family gets involved, and they get paranoid that I might be slipping in and out of sanity regularly. Not the first time I've been put into therapy because of this. It's like I'm the only one in my family that does this. Mind you, I'm only 1 out of at least 10 people, if you want to include relatives and/or in-laws, in the family. Reason for my initial concerns about this subject. Where family is concerned, I'm outmatched and outnumbered.
Sometimes, it tends to result in reactions like you'd see in some America's Funniest Home Videos, where a kid is talking or singing to themselves, or playing with imaginary friends, and once they notice they've been spotted, they panic; that's where I am, I'm the kid panicking. Considering I tend to have PTSD from having to deal with the worse psych, the -iatrist (the type that prescribe drugs), and a few other drug run-ins, and at least one of them nearly knocking me into a coma (for your safety, the brand was Geodon that hit me hardest, nearly putting me into a coma; a previous, and just as nasty one was Zyprexa), as well as slowing my mental faculties so much, I almost got put into special-ed in high school (despite being near-genius throughout home schooling (also according to standardized tests), and my first year returning to public), ugh. On one hand, I am happy to have made my mind really resilient by actually overcoming the drugs and recovering from them completely, and then some; but on the other, despite also self-administering psychological reviewing and so on, in order to prevent future events and encounters, even though acceptance is verbalized by nearly everyone I know, I still call bullshit (indirectly) because of their repeat concerns, and what essentially comes off as selective amnesia regarding the events and so on.
In a sense, I have a feeling that I am getting too smart at times, according to their perspectives, to the point that it's like I've been hiding so many problems from them for so long, I'm a Pandora's Box waiting to unleash Hell once opened. My problem with that view? It was opened since the first time I got bullied, and not even the school did anything about it. Hell was unleashed once I finally had enough of it, and decided to walk out of middle school un-announced, and take up home schooling. It even took the middle school half a year to notice something may be wrong; similar with some of my old school friends. Once they finally heard, no contact to see if I was alright. [sarcasm]Gee, thanks. I know I can count on you guys.[/sarcasm]. Back to topic, After hell was unleashed, I've spent my time since I started home school working on fixing myself from the inside. I had to lapse my sanity briefly so I can re-piece the fragments of it back together myself. Once that got settled, I was then able to keep a balanced, though rather unorthodox, mindset in my own comfortable style. Without the judgement of asshole classmates and useless teachers and principles and (mis-)guidance counselors, I was able to get things working to the point where I discovered my true self, and dis-illusioned myself from being "The Nice Guy". Then again, that image eventually turned into arrogance, and had to be taken apart one last time by confronting my innermost demons of bullying. What was initially going to be a standard internet attack from a website turned into a curb-stomp battle from my end essentially responding like a seasoned veteran that has experienced World War 3 in the manner of "That's it? That's all you've got? Who's really trolling here no,w because I don't think I was supposed to take on that role. I'm bored. Later.". Well, that's more or a summary of what happened. I jumped into a lion's den or a shark tank, and shrugged them off, and reduced them to their small fry counterparts because as a victim, I was disappointed by a vicious attack.
Maybe yet another reason I would not work in horror campaigns. I can look into absolute terror, and challenge it to a staring contest. Mindflayers would lose their minds if they were to even attempt to screw around with my mind. I've been through so much crap, almost nothing scares me even more. Even my worst fear of spiders. I am actually making it a New Year's resolution to try and finally make peace with them "Before the end". I'm actually getting tired of smashing them into oblivion, and asking forgiveness from them before I execute them; or even giving them a heads-up warning if I spot them, and spare them so I won't have to kill them.
Now that I come and think about it, I think my family's greatest fear is me turning into a Tyler Durden. Look, even I would find my own reasons to kick that guy's ass whenever it's necessary. Even an offshoot of my personality turning into one.
EDIT:
What really helps my perspective and psychological evolution is that my nephew is alot like me to many degrees (he's even starting to look like me when I was his age, it's weird). To the point that I can actually serve as a guide to prevent him from dealing with much of the same crap I had to with advice from experience (and in case he doesn't believe me, I let him to the hard way of experience), as well as being the judge in conflicts that can give a good disciplining where it belongs with justice prevailing (meaning, I don't play well to the "Boys can't hit girls" rule. Enforcing it only allows me to further investigate). Nobody gets away with crap around me, unless I'm feeling merciful. But even so, I still make things fair enough.
EDIT EDIT:
Said family member earlier did some searching after I called them out that I can't be the only one, and as the Google search showed (and I searched for it myself out of curiosity), the responses look similar to this board. Ranging from "no real problem." and "Not anything to really be worried about." to "Signs of advanced intelligence", "Self Therapy", and even the Talking to Himself trope (although that one is about voice acting), and a few stating otherwise and how to cure from it.
I love it when I turn up justified cases like that. Unfortunately, this thread is too new to be Googled.