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Its unlikely that the superficial clot has something to do with your dizziness
.Your dizziness could be due to inadequate hydration and low BP
.Please take plenty of fluids along with juices , lemonade to maintain adequate hydration and salts in your body.
A clot due to IV line would rarely remain for a month.So i advise you to get your bleeding parameters tested .Please visit your Doctor for these steps and reevaluation.