You have described a well-known complication known as extravasation of contrast media (iodinated contrast for CT or gadolinium for MRI, the latter in your case), which means some or all of the contrast which was supposed to be injected into your veins leaked out into the surrounding soft tissues. Patients typically experience localized pain, swelling, itching, and/or redness. In the vast majority of cases, the soft tissues just slowly absorb the contrast and everything returns back to normal over the course of several hours. Patient's may be provided with warm or cold compresses, although neither is evidence-based. In very very very rare instances, contrast extravasation may result in skin ulceration, tissue necrosis, and/or compartment syndrome (increased pressure causing mass effect on adjacent nerves and/or vessels). Patients should be instructed to seek medical attention if there is any of the following: increasing swelling or pain over time; blistering, ulceration, induration or other skin changes; and/or altered tissue perfusion and/or changes in sensation.
Bottom line: No need to worry! No need to go crazy! It almost always resolves w/o complication!
For more information, please refer to the American College of Radiology's Manual on Contrast Media, specifically the section on Extravasation of Contrast Media, available at: https://www.acr.org/-/media/ACR/Files/Clinical-Resources/Contrast_Media.pdf#page=20.
To answer your other question, it is unlikely to cause a deep venous thrombosis (DVT). However, there are various risk factors associated with DVT, one of them being long flights, with others including but not limited to prolonged bedrest, recent surgery, oral contraceptives, pregnancy, blood-clotting disorders, and cancer.
I know this was a couple of years ago but did you get any answers?? I have the exact same thing and I'm going crazy!