Good news!
"Inhalation does increase heart rate. This is due to a number of different factors including blood return and autonomic nervous system factors. The rate of increase is generally in the 10-20% range but it is possible to have higher increases (e.g. from 60 to 90 bpm) given the right circumstances. A greater increase in heart rate is actually a sign of good heart health."
http://www.medhelp.org/forums/cardio/messages/32980.html
It is very possible you felt your heart "stutter." Many, many people experience what are called premature beats. It feels like your heart is skipping, but in reality what is probably happening is your heart is beating normally, gets a little ahead of itself, throws an early beat, then you feel a pause (the stuffter), and finally, your heart kicks back into its normal rhythm. It is extremely common while we are resting, lying down, or just sitting. When we're busy and our hearts are beating faster, we either don't notice it, or it is not occurring at all.
The dizziness/faintness upon standing could be because of the change in BP because of the change in your body's position. You may notice the same sensation after getting up after being in the sun.
Store BP machines are notoriously wrong; however, I would follow up with a physician to be certain your BP is not bordering on hypertension (high blood pressure)
Hope that helps : )
connie