I dunno, maybe it's OK for you, the big wheels on a frame that small may force them to have the seat tube a certain height. As much as I dislike the small wheels for logistical reasons, for a person your size they can sometime allow for a frame geometry that works better. You might want to talk it through with the shop that sold it to you--here's how to picture it in your mind:
--on your (hopefully correct sized) road bike, when you add aero bars and drop your elbows to the pads, your position isn't quite right because you are folded too tight at the hips and your elbows are too high and too far forward.
--So you buy a new frame designed for the aero bars. The seat tube is angled more forward to unfold you at the hips and the top tube slopes down so the aero bars are lower than the saddle.
--additionally, the top tube is shorter to bring the elbows back so they are about 90 degrees and close to the kneecaps when riding
So, the big questions I would have are
a) is the angle at your elbows and shoulders correct
b) If you wanted the bars say 4 inches lower than the saddle would your frame allow this? It's a pretty reasonable position.
c) relative to your road bike, what is the difference in top tube length and saddle setback relative to the bottom bracket?
My gut feeling is having aero bars level with the saddle is fun for a while, but with practice you will want to be lower. If not, you might go just as fast on a conventional road bike.
If your road bike fits, take it in also and make sure this thing is right, it's an expensive bike.
ps could you have someone take a picture of you riding the bike on the trainer from the side