Not at all. You're of a healthy weight for someone your height - and I have seen jean sizes below 28 inch waist in shops before so honestly it's not that tiny at all x)
I get laughed at for having a 28 inch waist which is apparently tiny!?
Nope.
You're the same height as me, and slightly heavier (I was just under 10st last time I was weighed and have a 27" waist), and I'm perfectly healthy. I've been called skinny, but I definitely don't look (or feel) unhealthy. Though my looking fine might partly be because I'm quite broad.
I get laughed at for having a 28 inch waist which is apparently tiny!?
Hah I have a 27.5-28 inch waist and I'm 5FT 11 and people say my waist is to big. Seriously i myself and girls in my school consider 25-26 inch waist as as small anything more its big. I weigh 10.9-11 stones
You're definitely not underweight. Check your BMI (and IK it may not be wholly representative of whether or not you're a good weight etc.) but use it as a rough guide.