Are there any good ways to prevent goiter or hypothyroidism if I have an iodine allergy?

Techincally no such. You may be allergic to iodinated chemical compounds, such as radiographic dies, but you cannot be allergic to "the elemental" iodine, or iodine as a charged particle. Iodine is your thyroid, exist throughout your body, and you certainly can take in iodinized salt. This should not be a problem. Talk with your primary care doctor, an endocrinologist, or an allergy specialist, if you have doubts!
Iodide in salt. People with "iodine allergies" are actually allergic to iodine attached to large molecules, such as those used as contrast in imaging tests. They are not allergic to sodium iodide as found in most table salt, or most commercially prepared foods. It is extremely difficult to avoid iodine in foods.