Technical correction: You do have a sound card, it's just built in! (It's still considered a sound card, it's an 'onboard sound card.') At least I'm 99.98% sure of this.
Are you referring to the volume fading in and out?
If so, there's a few things you can try. One, it's probably the mic. If you went too cheap, you get too cheap. Reviews will help with that.
In my learning process, I first tried an onboard sound card. I had zero luck. I then got some cheap $20 card. I also had zero luck. I then bought a very, very expensive professional sound card - and I had zero luck.
It turns out, the 2nd one (the $20 one) was fine. I was just REALLY bad at it. With the onboard sound, I'd fill the buffer and get points of silence. That went away with the cheap one - and I suspect other problems went away but I was still too new to notice them.
The expensive sound card sits in a PC that I don't actually use. It made so little difference that I haven't bothered moving it. I also thought I had another buffer issue, but that was actually an Audacity timing issue that took some work to resolve and has nothing to do with your problem.
One of the causes might be electronic interference. Your devices are probably leaky. They're emitting all sorts of EMR. That could cause this problem.
What you can try is moving the mic as far away from the computer as the cord will let it go.
There's also the distance of the mic from the amp. You can try increasing that distance.
And, of course, this is really @MrHarryReems domain. He may think of something I don't know.