This might just be what is called an Intention Tremor.
In the absence of a Neurologist, it is easy to do a rough check. Get a partner/friend/whoever to sit in front of you a bit closer than arms length. The hold up one fingertip. With the first finger of the affected arm, you touch the tip of your nose, then their fingertip, back to your nose, fingertip, nose,fingertip, etc. The first clue is how soon you start to miss fingertip or nose.
Typically, the affected limb starts to move in a series of jerks or twitches, and this develops into (say) reaching for something and missing it. For a while you can cope by reaching “through” the object and closing your fingers when you touch it. It can get worse, so if it does look like IT - get it onto your record now (Neuro, MS Nurse, GP).