To get speed on your spins, your body has to be centered over your legs, and your core (torso) needs to be steady. Bringing your arms in can speed up the spin, but if your body isn't centered and steady, bringing in your arms won't make that much difference.
It really helps to practice spinning holding your arms out, in a T position, and spinning slowly - not trying right away to go as fast as you can. If you do that, you can learn to feel when your body is in the right position and is steady. Pull in your stomach and keep it pulled in, to help your body be upright and steady.
When you bring your arms in, remember to bring them in across your body. If you bring them in and raise your shoulders at the same time, your body won't be centered and you will lose speed in your spin.