Long-time solo guy here. A few ideas:
1) Find out if you tolerate and enjoy solitude. Try a few days alone in a low-risk environment.
2) Decide what level of risk you are willing to assume to do the things you want to do. Are you willing to die in the woods? Can your loved ones handle that? Do they respect your choice? The family issue is really hard for some folks to work out. Or maybe it doesn't matter to you.
I know this means understanding the relative risk of hiking solo against driving to work every day. Human beans are incompetent in assessning risk, and that goes even for policy wonks. Don't expect some factual statistic to give you an answer. Is air travel really safer than driving? By miles, yes, it is; by time spent in the air versus driving, no, it is not. Does that make any difference? It's up to you.
3)Assess your general risks and capacities: a)What do your recent physicals show? How do you honestly feel? Did you tell your doc that your heart that sometimes races? What about that pain you call indigestion? b) What are your physical limts? Do you have a high tolerance for pain? Do you stay calm when you are hurt? Can you self-rescue? These are things you have to answer for yourself with brutal honesty. I don't mean can you gnaw your arm off if trapped under a boulder, but more realistically, can you keep yourself alive with a broken femur until someone comes along?
A corollary to this is: will your family doc give you serious pain killers for your first-aid kit? They can keep you from going into shock and let you cope with the tasks you need to perform if you are injured. A few Percoset or Demerol can make all the difference.
4) Assess the risks inherent to every particular trek you consider undertaking in light of your capacities -- rejecting any tendency to set up a macho competition inside your head. Remember, if you are alone, there is no one around to dis you for being a chicken. (The corollary is, there is no one to hear you scream.) Bob's advice about ego is wise.
Bob mentioned stealth camping. Wise advice. My heirarchy of responses for dealing with the occastional nasty, dangerous folks I have encountered is don't be noticed, then fast feet (run away), fast thinking, and fast talking.
5) Get *trained* in wilderness medicine (as opposed to reading about it.) Then you can keep a minor problem from becoming serious and deal with serious injuries/illness so as to suffer fewer lasting effects.
*Solo resume' (not a brag, just to let you know that I have a little experience in this): by canoe up the Rio Grande, from the Gulf, by bicycle around the perimeter of the U.S., by foot on the AT (partly solo), the Big Bend, the Wiminuche, Pecos, Gila, Ouachita, numerous less august trails - over 40 years. Serious injuries: zero. Serious illness: zero. Treks terminated due to illness or injury: zero.