So I was conscripted into the church choir a couple of years ago, and as at the time they only had 2 altos they persuaded me to sing alto - and I love to sing the harmony line & my sightsinging has improved enormously but........the other altos really don't sing with any volume at all - I think they're singing but you have to listen really hard to hear anything much, so any audible alto harmony line depends on me (if I get lost & don't sing, the alto section dies ).
The problem is most alto lines seem to lie between G (sometimes F) below middle C and F or G above middle C and by the end of a choir practice I have no voice. Any time (infrequently) that we end up singing upwards from that I start to feel that I'm getting into a far more comfortable place to sing.

So, is it likely that I'm using my voice in an incorrect way and damaging it, or is it more likely to be that the range I'm using continually is simply too low for my voice?

There is a large chance that you could be damaging it. If you carry on this way it's possible that you will ruin your voice and will end up not having the option of singing soprano at all.

I had a similar problem when I was in my local musical theatre group. The director decided to start leaning towards "rock musicals" as the alto section was very strong and they all had voices to suit rock musicals instead. I was in the soprano section and everyone else sang very quietly, or at least could not be heard above the altos, so I really srained my voice trying to make the line heard, especially as I was the only one who could read music and therefore was the only one that actually knew the line in the first few weeks.
I left the group in the end because I didn't want to damage my voice and because I didn't really have time for it anyway.

Unless you feel an acute scratching sensation in your throat or larynx, you are not doing anything that will damage your voice. Singing this way will not prevent you from singing higher if your technique is solid.

However, as you're finishing hoarse after each session, there's clearly a problem in the way you're reaching your low notes - are you trying to push too much air to make them 'louder' or to project? Is your support working properly (bearing in mind that the role of support is to hold the air back rather than put it under pressure) ?

You can safely dispel any worries that it will harm your voice - no scratching means no permanent vocal damage, and you should have access to the low part (and even super low part) of your voice, irrespective of your vocal fach (fach's just tell us about the range where your voice colour sounds best, rather than any physical limitations on the actual range you have - but there is a great deal to be said aesthetically for singing where your voice sounds best of course!) - but you need to make the notes correctly to avoid hoarseness.

If you can record yourself singing one of the parts I'll happily give you some pointers and I'm sure the other teachers will too.

How does it feel after the rehearsal?

With good bottom notes, I often "help the altos out" but it leaves me feeling as if I've been growling all evening, and if I then have a good stretch into my soprano notes using sirening, or scales or anything to get me out of that pit, then I feel better.

There is however a big difference, being older my voice is more bomb proof, and can take it.

Warm up at home before you go. Take your voice up into your head register, then work on blending down into your chest working really carefully on finding the correct placing for each note. Remember how that feels, and end up by taking your voice up again.

Then go to the rehearsal. If you survive, then you can continue to sing alto. If you do not, then give up now before you kill off your soprano voice or do some damage.

I have found exactly the same problem in my school probelm because people do not sing loud enough and I have strained my voice several times in the past which worries me qite a lot now I realise I mgiht seriously have damaged my voice. I agree with the other advice-sing quieter or don't sing alto.

I think it's important to distinguish between volume and projection.

If we bear in mind that the voice has several configurations possible in the vocal folds (thick, thin, rigid) - ladies who sing classical generally only learn to use the thin fold setting - low notes, if they are to be sung loudly - MUST be sung in the thick fold setting to avoid vocal damage from over pushing the thin folds. Therefore, if you want to make yourself louder - use thicker vocal folds and not more pressure or air. If you want to be heard without using thick folds, use projection instead, which you should be able to do at all volumes from pp to ff.

You'll never be able to sing loud enough to carry in a large space - the human voice can't do that, but you CAN project well enough to be heard in a large space, so choose projection over volume, but if you do have to sing low and loud (rather than low and projected) then use thick vocal folds - trying to push volume through thin folds will almost always lead to hoarseness.

I agree with Jod and would go further and say this. I would find another choir ASAP or group to join where you can sing in your proper register. The choirperson might want to put pressure on you to stay but that is his problem, your agenda is to look after your voice