@dilerycorona Welcome to BassBuzz!
When you have time, join us on the Introduce Yourself! thread.
No one online can, definitively, tell you whether you should get it checked out by a doctor, or not. My suggestion is, if it hurts and it keeps you from playing, get it checked out by a Hand Specialist.
As to small hands, there is a myth that people with small hands can’t play bass. This is completely false. If you search YouTube you can find small children that kill on a full size bass and their hands are tiny. For some reason people like to tell other people what they can’t do. I have larger man hands and someone even told me my hands weren’t big enough to play bass. (That guy was a jackass about lots of things.)
As to the pinky, almost everyone has problems with their pinky. It’s just been sitting there for your whole life, never being asked to do anything on it’s own. It’s only natural there would be a steep learning curve for the little guy.
This is what makes me think you’re doing fine. I play, almost, everyday until my hands get tired and I frequently play till my fretting hand cramps. (The bass line for Billie Jean is a hand killer.)
Also, most new players fret notes too hard and hold the neck too firmly. If you can practice holding the neck without using a death grip and only using as much pressure as you absolutely need to get a clean note, this goes a long way towards saving your hand strength for longer playing times. However, this is much easier said than done. Most of us, when we get excited, go right back to strangling the neck like we’re trying to kill a duck.
Lastly, don’t let this discourage you from playing. We have had plenty of people on BassBuzz with various health and hand problems (including missing fingers). The joy that comes from playing is worth so much more than the temporary frustrations that come from getting there.
Let me know if any of this helps.