I totally do not see where you look older. To my eyes, you look younger. You do not look sickly. I think that when we first lose weight, our face changes suddenly, our skin hasn't contracted yet, and our loved ones might see those as scary changes. Everyone says your skin rebounds some and tightens, faces fill out again, etc. So maybe just give it time and let them catch up to the new you.
It's hard for us to accept those comments as concern, a lot easier to think it's criticism, but I think with most of our families, they speak out of love and concern--and probably end up doing it badly!
You do not look old. You do not look "too" skinny. You look great.