I recorded me talking/yelling to try out my new mic. I am wondering if I could increase the talking while keeping the yelling the same volume. Some parts are really quite but when amplified (by selecting the couple of seconds and then amplified) is normal talking volume.
You can use dynamic range compression to make the difference in amplitude between the loud and quiet parts smaller. This is the most common solution for your problem, and it is used everywhere from broadcasting to film and music production. (audacity has a compressor in the effects section)
You can learn how to use a compressor here. If you want to affect the peaks as less as possible, you can try parallel compression (a specific type of dynamic range compression).
Another solution is automation. You manually set an amplitude envelope to be lower in the louder parts, and higher in the quiet parts. You can do this with Audacity's envelope tool.
That process is called compression -- not data compression as in MP3 etc, but level compression. Look in the Audacity 'effects' menu for "Compressor..."
I would definitely use automation for this because you can easily boost whole sections of talking that way without affecting the yelling section at all - using a compressor will boost the quiet parts Relative to the yelling, but what it is actually doing is squashing the yelling and will change the sound of the yelling depending on the settings.