Skim milk contains 7 milligrams more sodium than whole or 2% milk which is not a significant difference. What is more important for you is getting an adequate intake of calcium, riboflavin, vitamin A and vitamin D.
Since you are overweight, skim milk is better for you to drink. Skim milk is actually whole milk (3.5%) with the butterfat removed. This amounts to approximately one and one-half teaspoons of butter or 90 calories. Otherwise, skim milk has approximately the same composition of other nutrients. Adults should drink two cups of milk per day unless they are allergic to milk or have lactose intolerance.
To help wean yourself off a higher fat milk, try drinking 2% milk for one week, then drink 1% milk for one or two weeks and finally start drinking skim milk the remainder of the time. Over time you will become used to the taste of skim milk and higher fat milk will taste like cream to you.