Kit, the heart rate of a woman (I think you are female, else it's a bit lower) should be between 60 and 100 beats per minute. It is desirable for it to be low. Your age, size, activity level and other things such as medication can affect it. It would be good to see a doctor if it's above 100 a lot. You can take your own pulse very easily. The suggestion usually is to feel it on yourself (there is areas on the wrist, throat and probably other locations where you can feel it, I suggest to look it up online), set a timer for 15 seconds and count how many beats you can feel, then multiply by four. This gives you the heart rate. If you find that it's often in the range of 100, especially if you've been sitting for a few minutes, I think seeing your GP would be a good idea. But it's not immediately dangerous.

Btw the thing on the finger is most probably both pulse and oxygen saturation.