I've also been skating 3 years, and am a 50+ skater. It took me a LONG time to be able to step on the ice and just "go". Even now, I still need to hold on to something while stepping onto the ice...either the frame at the entrance, the wall at that entrance, whatever. I cannot just step onto the ice free-handed and start zooming off. So, what I do (maybe to make myself feel better, lol) is that I enter the ice from the barrier entrance. I immediately stay right by the barrier and do some warm-ups. I "test" the ice right there for a while, even if it's only a few minutes. Then I do slow, steady strokes around the whole rink 2 or 3 times. By that time I feel ready to tackle the stuff at the level I'm working on. I wouldn't say I feel "wobbly" at first, I'm not shaking or have unstead feet, but just not ready to go zooming off right away.
So, long story short, you are not alone!
Rene