Is it safe to travel if my spleen and liver are swollen?

Yes: However, you should take general precautions to avoid the risk of a DVT (deep venous thrombosis, or clot formation) by getting up and walking every two hours, especially if you are overweight, smoke, use birth control pills, have cancer or a history of dvt.

Preferably rest: Your car? Probably fine for short trip airplane? May want to get well.