It's hard to give a full an accurate answer to this question, because it depends in a lot of matters. As a guitar player, but not professional, over several years I also have experienced different episodes of "physical" problems, related with or partially influenced by guitar practicing time, so I will try to give you my point of view in these matters, hoping this could be helpful for you now, or in the future.
It could be hard to find a specific cause for the pain you describe, starting not even for the necessity of watching you playing several times to evaluate your "attack" to the string, and describe if it's a good or bad practice, but even more for the shape and physical appearance and form of your fingers. It's always useful to have professional or experienced guitar player advice watching you playing, to learn how to avoid bad practices, and streghten your way of playing. But, it is a true fact, that this should'nt be enough and could not solve your problem.
On the other hand, because each one has it's own muscular complexity and physical structure, and it would be really hard, but not impossible, I guess, to find someone who a physical profile in common with you, tand hat could register same feelings or trouble. On the other hand, it's possible that other person have experiencied same pain even having physical differences, and that is the most important thing, because, from my side, and based on my experience, most people that have not experienced same problem as yours, would find it difficult to help you solving the exact problem.
Maybe the best option, if the problem persists over, let's say, a year of daily practice, should be to ask to a traumatoloy specialist, or even a physical therapist, with some experience on string intrument playing, but I'm afraid this professional profile it would be really hard to find.
Bearing in mind all of this, and taking the problem as my own, I would consider doing the following:
- Find a good guitar teacher that could analize you particular case and give you advice about good posture, ergonomics and fingerpicking best practices (I found that good classical guitar teachers usually take care about these issues) and invert in some on-site (recommended, if possible) classes, to try to find out.
- Keep your daily practice time, and maybe add some more exercices aimed just for fingerpicking, to help generating calluses and reinforce skin on the fingers.
- Find out if there is any physical exercise that could help you develop muscles around the affected area (helped me a lot in some cases, but couldn't be sure if this is possible in your case, as I'm far from an expert on this matter), or just to warm-up before fingerpicking exercices.