Same thing happens to me, I am 30 weeks. Most of the time it occurs when I am already sitting down and its especially awkward becoming faint and dizzy on my way to work on the train. My limbs also feel severely heavy and achy and I am constantly tired. I've had blood tests done and there is nothing abnormal with my iron levels. You should definitely have tests done again just to be on the safe side. My midwife suggested to take things slower, drink plenty of water and eat smaller but constant meals through out the day. Hope you feel better soon!
Definitely go jn for blood work. You might be low on iron and have anemia. If so all they'll do is have you get more iron in your diet thru iron supplements or food. When you feel dizzy and faint, lay in your left side. This increases blood flow to your heart and you can also lay on you back on the couch or floor with your legs propped over your head. This helps more blood get to your brain. Drink lots of water. Like a gallon a day. That'll help and you can try eating foods higher in sodium, more small frequent meals. These things will help bring up your blood pressure if that's the issue. I was having these same problems, got all my blood work done, it all came back normal. I was getting dizzy and faint. Laying on my left side, drinking lots of water, and eating foods higher in sodium helped me.
I would go in. It could be your blood pressure which can get dangerous.