Hello Asia,
Tapping like this isn't something you've probably ever done much of before... it's likely that your hands and wrists may take a little time to adjust, especially if you're doing it more often and "enthusiastically" as you say. It could be that maybe you're tapping a little too hard -- and if so, you can lighten up a bit... maybe massage your knuckles; stretch your hands and wrists between tapping; or just back off a bit.
WITH THAT SAID... what I really believe is happening, is that you're naturally finding your alternative tapping points! When I first began working with EFT, I made some major breakthroughs by noticing when/where these little pains began to pop up -- and using them as "alternative" tapping points in addition to the EFT basic recipe. Go ahead and tap directly on them (but also keep doing the basic recipe). For me, they always (surprise-surprise) corresponded perfectly with some published acupuncture meridian point.
Now when I tap, I notice all sensations immediately -- even if something just seems like a small "itch" -- I follow it... allowing those sensations to guide me as to where I need to tap. It's also a great way to "Chase the Pain". For me, I find that when one of the tapping points is sensitive, it's because something is blocked there, and I tend to tap longer on that point -- which then clears completely. I experience that a lot when using the Karate-Chop point, the 9-Gamut and many alternative points on my head and face. I typically check the tapping points on both sides to see whether one side might be more sensitive than the other -- in which case, I always choose the spot most "sore" to tap on, regardless of which side I'm doing my general tapping on.
There are websites you can search online that post fairly detailed pictures of where the acupressure meridian points are.
I hope this helps!
Kindest regards,