A non-competition agreement *is* an agreement: that is, it is a contract, or something you agreed to. You can't be stopped from working for someone else unless you signed a non-competition agreement; and if you did sign one, you are only limited to the degree or in the ways that the agreement, by its plain language or terms, limits you--that is, they can't impose broader limits than those to which you agreed in signing the agreement. On the other hand, if you did sign, at the risk of oversimplying somewhat, they can enforce whatever terms you did agree to, even if it means not working for certain other companies in other positions. So you need to look at any non-competition agreements you signed; you can be restricted in those ways--and only those ways--that the agreements say you can be. The agreements' terms will control what you can and cannot do.