Hello,
If the blood pressure cuff is inflated to the point of being uncomfortable and too tight, you could get the petechiae. Maybe the nurse doing the blood pressure is taking the cuff up higher than need be, thus, causing the bruising and red marks under the skin.
You may also be bruising easier than before due to lack of nutrients such as bio-flavonoids. These work with vitamin C and if your system is low, you will definitely bruise easier and have this issue