If you were standing, then make sure that you're singing with the correct posture. It will most definitely change your sound.
As you grow, your vocal folds (voice box) develops. The more you sing a lot of higher notes that's not straining your folds, the better. When you sing higher, your vocal folds stretch. At first it would sound breathy because it isn't closing/fluttering correctly, but you'd gain the muscle needed as you practice. Do you mind me asking how old you are? (:
Tenor... No. Plus, most woman should not be categorized around that range. If anything, you'd be a mezzo soprano. But you have the timbre (sound) of a soprano.
There is a number of reasons why your voice is fatigue after singing.
1. Posture. If you don't carry your instrument correctly, you can break it. It's important that your flow of air is fluid and precise.
2. Working for your notes. There are some singers, like I, who work for their notes rather than let the notes come out. If you feel yourself using too many muscles around your larynx area (where the vocal folds are), then you must stop. The more you work for your notes, the more you're likely to gain disorders. I, myself, have a dysphonia voice disorder. I'm a dramatic (viking-sounding) soprano who worked for most notes and sound. Now, my voice is completely different. I can still have the same dramatic sound, however, I'm sometimes very thin. Almost like a coloratura (flutter-like soprano).
3. Speaking range. Sometimes people don't speak in the same range they sing. You may sound like you sing high, but you could be speaking low. If you do speak low, I would recommend shifting your speaking range higher. This will help you keep off your vocal folds and give them rest.
4. Warming up. If you just sing songs without warming up your vocal folds, this can cause a lot of damage. Your folds don't just naturally stretch or widen. You have to progress it little by little with vocal techniques. Usually going from 1-5-4-3-2-1 usually helps. So if in the key of C, you'd sing C-G-F-E-D-C with pitch using different vowels such as AY, EE, OH, OO, AH, etc... But always warm up no matter what. It will save you in the long run.
I would say no to singing softer. The softer you sing, the closer it is to a whisper, and whispers are terrible for your vocal folds. It's kind of like sandpaper rubbing against it. The best bet is to give your voice a rest at times and just not sing. So if it is raspier on a certain day, just lay off it.
I hope this helps!
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