着急 and 担心 have nearly the same meaning. Both of them mean that you are worried about somebody. In this case, they are interchangeable. For example,儿子没有回家，妈妈很着急/担心. 紧张 is a little bit different. We often use it to describe our feelings before an exam or an interview. It emphasize the feelings of nervous more than worried.

着急 means hurry. 不要着急，don't be hurry. 担心 means worry. 别担心，don't worry. 紧张 means nervous. I'm nervous. I hope it could help for you.

紧张 = nervous 担心 = worry / worry about 着急： we can use this word for two cases: 1) when we have no time. for example, 他现在很着急，因为他就要迟到了。----he is very 着急 now, because he gonna be late. 2) when we are worrying about something. for example, 他现在很着急，因为他找不到他儿子了。---he is very 着急 now, because his lost his son.