Summer Internship

It depends what state you did your internship in. If it was TX, no. TX does not have a state income tax.

If you're filling out a federal income tax form, yes, you have to add it to your federal income. If you didn't receive a W-2 form, contact the company and request a copy of it. 

If your internship was in a different state, you may have to file a tax return in that state. To find out the income tax filing requirements for the state, contact that state's Department of Revenue. Click here.

My internship was in Texas, where I live, and I made $550. They haven't sent me anything. I believe I need to do my state and federal taxes. I've bought Turbo Tax I just need to fill everything out. However, the office I had my internship at has not sent me anything. 

Even though they did not send you anything, you still need to report it since it is income you received for performing a service.  Here is my best suggestion.  

1. Since this is earned income where FICA taxes weren't reported, go to federal>wages and income>Self-Employment>Self-employment income and expenses>start
2. Did you have any self-employment income or expenses? YES
3. Then the program will ask you what type of work it is indicate it is an internship
4. and then go through the questions and answer as generically as you can
5. When you finish your profile you will arrive at a screen asking you about your income. You will indicate this is Other self-employed income. Includes 1099-K, cash, and checks. 
6. Now if you had expenses against this income, there is a place where you can record this but if you do, Turbo Tax will require you to upgrade to Turbo Tax Self-employed. At this point, it may be worth it just to claim the income and not the expenses.  This is because the tax generated  on this little bit of income may be less than upgrading your product. This is a choice that you must make.