To answer you question: No! Pain, numbness, tingling, fatigue, and strain are not "normal" and should be avoided at all costs. If you are weak and sore after only 10 minutes then something is very wrong, that's a huge red flag. Playing the bass should take about the same amount of force as typing on your computer keyboard, and you should be able to play the bass for an hour (or more) without any fatigue.
Two things you want to check out:
- Make sure your bass has a good "set up" with strings that are comfortable for you, and an "action" that is easy to press the strings down to the frets. Again, it should be about the same effort to fret a note as to type a letter on your computer keyboard. If it requires significantly more force than that, then your bass is not well "set up."
- Check your technique! A good teacher is really, really useful for not hurting yourself when you're starting off. And/or to supplement your lessons, go on YouTube and study the technique of pro players with long and successful careers. Without seeing any photos or video of your playing, the best advice I can give, is turn up your amp and play with a lighter touch! Your fingers should just lightly touch the strings, no need to "dig in," let your amp do the hard work. If you watch most pro players on stage, they are very relaxed and not working hard at all to play the bass. If their playing style seems aggressive and overactive (like Flea) then usually that's just an act, part of the show.
Here is my immediate short term suggestion (which I know might be controversial):
For right now: If it hurts to fret a note with your 4th (pinky) finger, then shift/move your entire hand, and fret that note with a "stronger" finger instead.
Lots of very successful pro players, including Geddy Lee, Tina Weymouth, and Rocco Prestia, seldom fret with their 4th fingers. There is no "need" to use your 4th finger, to be a successful bass player at the highest artistic level.
Especially if trying to use your 4th finger is damaging your body and potentially putting your guitar career at risk! How are you going to fret chords on the guitar if you injure your pinky? Feel free to study players who
don't use their 4th finger for now, and then later in your learning process, there will be plenty of time to study players who
do fret with their 4th finger.
As a general learning philosophy, I believe it is more important for beginners to learn
something than for beginners to learn
everything. "Someone" told you that you are "supposed" to use your 4th finger instead of your 3rd finger (even though it hurts). They are giving you
terrible advice in my opinion. Any time an internet stranger gives you random advice
always fact-check that advice against YouTube clips of your favorite players. For example if a random stranger tells you, "you need to fret with your pinky" then go on YouTube and study your favorite players: Do they universally follow the random stranger's advice of always fretting with their pinky, or do some pros, in fact, fret with their ring fingers instead?
For now, just pick some easy songs you can play with 1 or 2 fingers, no strain or fatigue, and have fun learning at your own pace, injury-free! For example, every Talking Heads song ever written can be played without using your 4th finger; that should keep you busy for at least a few weeks, right? Songs like "Once in a Lifetime" and "Psycho Killer" are real crowd-pleasers, and there is nothing in your technical skill set holding you back from learning those songs right now, if you choose.
If you can play an easy song like "Mary Had a Little Lamb" in a state of total relaxation, without any stress in your hands or fingers, then I am proud of you: you are on the right track and making good progress.
