Sleeves come in different sizes and different levels of compression. Most of the time we use a sleeve 20-30mmHg for arm lymphedema. If your hand swells you need to wear either a glove or a gauntlet which is a glove without fingers. A variety of brands exist, and the shape of your body would determine which one might be the most comfortable. For example, the Juzo brand comes in a short length and has a “max” size that allows for a wider upper arm. The LympheDIVA brand works well on longer and leaner arms. The Medi brand has a bit of pressure relief at the inner elbow. It can be quite helpful to visit a durable medical equipment store that sells these items so you can see and feel the differences between brands.
In regard to the steam room, if you have been using this with no adverse effects to your arm swelling, then you could continue to use. But be observant to conditions or activities that tend to increase arm swelling. Then take note and either avoid those situations or wear compression to avoid increased swelling in the arm.