Indeed the First Amendment protects the freedom to assembly and associate (among other things like speech, religion, etc), which is why labor unions are legal and protected. However, just like we have the right to not speak, we also have the right to not associate. This means that an individual should be allowed to chose whether or not he wants to be part of a labor union to begin with. Some pro-labor activists cite the "free rider" problem as a reason to oppose right-to-work legislation. They say the free rider problem is that those who choose not to associate with a union are still reaping the benefits on behalf of the union who collectively bargained for its members. This is an exaggerated hyperbole by the pro-labor movement, in my opinion. Members of a labor union don't get any fewer benefits because someone is choosing not to associate with that union. The leaders of the union may be getting fewer dues, but the members are not receiving any fewer benefits because someone chose not to associate and is still reaping those benefits. In order for them to be losing said benefits, they would have to have had them to begin with. Since the employer is the one who owns all the profit, it is his/her decision alone whether or not to include benefits for those who have chosen to associate or not associate.
The First Amendment protects freedom of speech, freedom of the press, freedom of assembly, and freedom of religion. The right to work is not listed in the text of the amendment. A new constitutional amendment would have to be made if the right to work is going to be protected.