Amplification is nice for singing because you can add a little reverb (a mild echo quality that makes you sound like you're a professional, singing in a hall). It's really cool; and the day I got a mic and a small amp with reverb was the day I stopped sounding like someone singing in his bedroom, and started sounding like a singer.
Having noted that, I think if you're having trouble hitting the higher notes with the forceful command singing is supposed to entail, then two things might help: One - practice, practice, practice! ..I had trouble with higher notes at first, but I wouldn't accept being unable so I sang the same thing over and over, making funny faces from straining to get it done, until it became easier. But it did get easier. You're breaking in some muscles that have never been used much, and so have little strength..so hours of practice daily may be needed to build them up.
And the second thing I'd suggest is for all of us there are some songs that are "out of our (comfortable) range"; and we just learn which kinds of songs we should avoid because they don't fit our individual range.
But hey, don't take no till you've tried I say!
And as for the volume of singing, there are some songs and types of music that are more quietly done than others, yes, but in general I find that well felt and done singing is usually about as loud as yelling (or so my neighbor tells me! 0_o )
Being in the same room as a professional singing even without an amp is generally enough to make a shiver run up your spine (a good one) from the sound waves going right into your bones! And singers are like that. Big mouths, big lungs.. Of course not everyone is physically a powerhouse, but when those things are lacking then BIG SPIRIT can get it done! So don't give up, Do what you love. Just practice a lot, and - as my music teacher always told me - "belt it out! Sing it like you mean it!" ;)