Does the position of my arm and body matter?
If yes, then how?
What's the best body position for measuring the blood pressure?
While trying to measure the blood pressure, the physician is most likely interested in measuring the pressure inside the left ventricle of the heart. So it is necessary that the Sphygmomanometer and the cuff should remain at the level of the heart. If it is above the level of heart, the reading is likely to be low, and if it is below the heart, the reading is likely to be high. Also, the blood pressure varies with the posture of the body in which the measurement is taken. So the blood pressure value that exists in most guidelines (for example JNC 8) is measured in the sitting position. Hence the value we are intenting to measure is the one with the patient is sitting position, back supported, legs uncrossed, and upper arm bared. The diastolic pressure is high in sitting position, and systolic pressure is high in supine position. Not supporting the back will increase diastolic pressure, while sitting cross legged increases systolic pressure. This is due to the inherent mechanisms in the human body to maintain perfusions to certain organs. The detailed biomechanics is beyond the scope of the present discussion though.
Reference : New AHA Recommendations for Blood Pressure Measurement
There are numerous factors that can affect blood pressure from body position (as you mention) to stress or pain. The most important thing one can do is try and take the BP measurement the same way every time. I also think it can be beneficial keeping a journal with some additional information next to the BP. For example, if you are in pain, then make a note of that (e.g., right shoulder hurts today, 5/10); or if you are very fatigued or sick that day, note that as well. I would also always include the time of day.
Even in medical offices with trained staff, it can be tough to obtain BP measurements that are done 'perfectly.' See this article from Hwang et al. (2018) on the issue of mistakes when taking blood pressure readings. That said, here are the guidelines from the ANA on taking BP readings: ANA BP Readings. So, individuals taking home BPs don't need to stress out about being 'perfect.'
Interestingly, in adults it doesn't seem to matter if you take the BP reading in the right or left arm, just that it is at the level of the right atrium (midpoint of the sternum); however, in children, the recommendation is to take the BP in the right arm. Further, if there is obstructive arterial disease present, then the location where the BP is taken does matter.
References
Hwang, K. O., Aigbe, A., Ju, H. H., Jackson, V. C., & Sedlock, E. W. (2018). Barriers to Accurate Blood Pressure Measurement in the Medical Office. Journal of primary care & community health, 9, 2150132718816929. https://doi.org/10.1177/2150132718816929
Muntner, P., Shimbo, D., Carey, R. M., Charleston, J. B., Gaillard, T., Misra, S., Myers, M. G., Ogedegbe, G., Schwartz, J. E., Townsend, R. R., Urbina, E. M., Viera, A. J., White, W. B., & Wright, J. T. (2019). Measurement of blood pressure in humans: A scientific statement from the american heart association. Hypertension (Dallas, Tex.: 1979), 73(5), e35–e66. https://doi.org/10.1161/HYP.0000000000000087