If you have a mild to moderate contagious disease, is it immoral to go about your ordinary business knowing that this will expose other people to the disease?

There is not much you can do about colds. They're incurable, they're usually only minor problems, and in some cases you have no choice because some things have to be done, they can't be put off and we can't be quarantined until the disease runs its course.

Before we had the capacity to quarantine people - because it's possible for them to get some kind of compensation so that they don't starve from lack of funds while quarantined - and had no way to isolate them we generally required those who might be affected to be warned. Thus we have the term "leper's bell" in which those who suffered from leprosy (what we now call Hansen's disease) would wear a bell to be able to warn people to stay away while they passed through an area.

It was the best we could do under the circumstances.

In some cases it might be unavoidable. If you know you're sick with a cold and cannot afford not to work, if you live in a very poor country you might not be able to get anything to allow you to protect others; there is nothing you can do. Unless other people are willing to subsidize you until you're over the disease, they have no right to, in effect, ask you to accept a death sentence by starving in order to stay away from others. But that also means to the extent you can prevent it, you don't have the right to intentionally injure other people.

If you live in a slightly more affluent country but still have to work, you might decide you want to get a face mask to protect others. You have no choice but to expose other people to your illness on the way to get that mask. But by getting that mask you now have the capacity to wear it and no longer expose others to your illness. In such a case, your effort to go get the mask is a reasonable solution to the problem.