IMO, if you go into a new project with the idea age will hold you back, then age will hold you back. You've already set yourself up for some degree of failure and you've provided yourself an excuse for why you didn't succeed. Of course, being realistic about what you're facing is in most cases the best advice. I no longer get up on the roof to put up Xmas decorations or even climb to the top of a 26' ladder because I have a funky knee that I don't trust to catch me if I make a misstep. Your risks when picking up an acoustic guitar are far less grave.
I read this article the other day and realized I didn't even know there was a 100 plus age bracket in track and field; https://www.washingtonpost.com/news/ear ... 56d89f1183
Therefore, without getting into a Henny Youngman joke, age is simply what you believe it to be and it should never stop you from doing anything that doesn't risk your well being. Learning to read notation is far less difficult than, say, learning Italian.
I have to ask though, if you've been practicing for "several months" and you know you will need to learn how to read notation to successfully play classical guitar, what has stopped you from starting on that bit of education?
Excuse me if I apply a little personal anecdote to this situation but I've known several people who have decided they wanted to do something or to learn something though their desire was really just to have an excuse to go out and acquire something fairly expensive. They never really carry through with the rest of "the plan" after the item has been purchased.
Therefore, my first piece of advice would be to put off buying a new nylon string guitar until you can proficiently read notation and play the Major scale from memory. IMO playing from TAB is a snap if you can first read notation. So there's your first bit of analysis based on your op, you have never succeeded at doing more than diddling on a guitar because you've not set proper goals for yourself when it comes to playing the guitar.
Put two items into a search engine; 1) how to set realistic goals, and 2) how to create and use a musician's practice journal. If you can't follow through on either of those two goals, then don't bother thinking about buying a new guitar. You don't need anything more than your present guitar to follow through on those two items and you can test your staying power by both learning how to read notation and how to play a Major scale. Even if you decide to never play a classical piece, you'll still be ahead of the game if you accomplish just those two things.
Regarding any issues with your fingers/hands, you may have simply overworked your hand on one day and caused temporary inflammation. Or you may have fallen into such bad habits that your technique is sorely lacking and your hands are suffering the consequences. If this was a one off incident, then I would bet on the former. Remember, you cannot make up for three days without practice by playing for three hours on one day. If this is more constant, then you first have to deduce the cause of the discomfort. Start from the very beginning lessons to check your technique. Make sure your posture is correct and you are holding the guitar in a "correct" position. So on and so on. If the discomfort is anything more than temporary - a lot of us wake up with stiff hands when we are in our 60's - and you cannot play well due to stiffness, then you need to consult a physician who does more than tell you it may be a bit of arthritis. An orthopedic surgeon familiar with injuries related to age is your first choice since orthos familiar with musician's injuries are very difficult to run across.
If you are at the beginning stages of arthritis, then you need a plan for dealing with the issue. If you have developed tendonitis or a trigger finger, then another plan is in order. Either way, the discomfort and stiffness is related to inflammation and each will have short and long term strategies to deal with the situation. Guitar forums are full of advice for hand and finger issues but your best bet is a physician familiar with age related issues IMO. Get a diagnosis so you know with some certainty what you are dealing with and not just guessing and hoping it goes away.
A portion of your practice journal should be set up for warming up, which can be many things depending on your progress and your physical abilities. Set realistic goals, put them in writing in your journal and maintain a record of your practice sessions.
None of this requires you use anything more than your present equipment. There's no need for an instructor at this point unless you feel you can afford to pay for lessons and you do not feel intimidated by a teacher three or more decades younger than yourself. Give yourself a few months to get up to speed with notation and scales and, if at that point, you still feel as though you wish to play more serious music, then you can decide where to go next.