I feel you, recently my cat died and it has had me thinking more about the mortality of my other loved ones, my parents, my brothers and sisters etc. I don't let it get carried away because it's certainly not fun to worry about. Your anxiety sounds out of control, and you are essentially living your parents deaths over and over, suffering some of the pain repeatedly and unnecessarily.
I definitely think you should consider getting some professional help. If you cannot or will not for whatever reason here are some suggestions.
1) Try this. Sit down for up to an hour or so at a time and imagining your parents dying. Imagine the pain, imagine the loss. Do not turn away from the uncomfortable feelings, the fear. Keep focusing on them and face the fear. While you do this, repeat the notion to yourself that all life can be lost at any time. "At any moment, my parents could die." This is true, this is just a fact of life. What you are trying to do is accept this basic truth about life, that yes your big fear can happen at any time like it can for anyone.
What should happen to you is that the fear you have, by immersing yourself in it and facing the feelings and fear head on, should become more boring after a while, and cause you less anxiety.
2) Try to list all the things you like and enjoy in life, that are independent of your parents. Sure, the loss of a parent or parents can be devastating, but what you are doing is "catastrophizing". Yes it will hurt when it eventually happens, but most likely you will be able to go on, and there is plenty you enjoy about life that is independent of your parents, and that you could still enjoy even if you were to lose them. Try to be reasonable about things, you will lose some thing sure, you cannot visit them, their memory may cause you pain, but there are obvious things you will not lose. Many of them. For example if you really like a certain food, you will still be able to eat it. If you like certain activities you will still be able to do them. If you have more than one loved one or friend in your life you'll likely still have most if one passes away....
As for the anxiety caused by financial fears you should try some of the same. At any time anyone no matter how rich, can lose it all. Repeat this to yourself till it becomes more mundane. Then list the things you can do about it if it happens. Note that even if you lose all, you still have future earning potential. Think about no matter how bad things get, you'll probably be able to provide for yourself, if perhaps not comfortably at times. Think about the good will of other humans who would often help you if you were in dire straights. I've been there, I have been a homeless teenager completely alone in cities where I knew not a soul. Despite not wanting help from anyone and not seeking it the kindness of strangers was vital to me more than once. No matter how alone you feel you aren't, and if things get real bad for you there are many kind people who would be happy to help (there are plenty who wouldn't too, but as long as good people exist in the world you do not have to despair about the bad ones).
Beyond trying to get your anxiety about your financial security under control, you should work on getting your financial security under control. Save up some money. Figure out what you absolutely need to live. The food you need, the cheapest shelter you can afford etc, and figure out how much that costs per month. Then try to build up an emergency fund. Unless you have high-interest debt (and sometimes even so) this is your #1 personal finance priority and it will dramatically impact your anxiety about financial things. Even if you just have just 3 months worth this is a HUGE security net and can help you through most common speed bumps in life. Losing a job is a common one, and having 3+ months of an emergency fund makes that much much easier to deal with. Shoot for having a longer emergency fund of at least 6-10 months eventually, with this you can survive almost any financial scenario with a lot less worry and pain than without. Once you have this you need to start investing in your future retirement funds etc, but the emergency fund will take a ton of the edge off day-to-day anxiety about finances.
Let me know if you have any questions or if you are interested in more information. I would like to repeat the suggestion that you seek professional help for your anxiety as it is disrupting your life. Professional help will likely come in the form of some cognitive behavioral therapy similar to the exercises I asked you to try, where you try to recognize the unreasonable thoughts and work to change them. But it may also include medication that can dramatically help you deal with the anxiety, which might be medically necessary for you and that people on the internet cannot help you with either in the diagnosis or the providing of the treatment you need.
If you are interested in learning more about dealing with your anxiety on your own I would recommend the following book as a starting point: The Worry Cure: Seven Steps to Stop Worry from Stopping You
by Dr. Robert L. Leahy.
Good luck! I'm rooting for you and if you have any questions or want more information just let us know!