Any blood clot that you have should be discussed with your primary care doctor
to make sure that it is being treated appropriately. Fortunately, clots in the arm are much less likely to spread to other parts of your body and to grow themselves, and so the decision to watch them closely is often the best choice for many patients.
If you have met with your doctor and that was the choice that you agreed to pursue, then you should feel comfortable without altering your diet. Some of the most healthy foods, such as spinach and other green, leafy vegetables actually help your body to clot appropriately, but your doctor would usually not advise you to avoid these because you have a clot. Instead, if the clot was a medical issue, your doctor would prescribe the use of appropriate blood thinning medications. Food and diet alterations are not used by physicians for the purpose of dissolving clots.
Aspirin is one common medication that is available over the counter and does stop your platelets from functioning properly, but, like all medications, it should not be started chronically until you have discussed this with your doctor. Stay active, eat healthy, and continue to follow up with your doctor who is treating your clot.