No license needed.  

To report your self employment income you will fill out schedule C in your personal 1040 tax return and pay SE self employment Tax. You can enter Self Employment Income into Online Deluxe or Premier but if you have any expenses you will have to upgrade to the Self Employed version. Or any of the Desktop programs. But you will get the most help in the Home & Business version.

How to enter income from Self Employment
https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/...

You might want to use Quicken or QuickBooks to keep tract of your income and expenses. There is one called QBSE QuickBooks Self Employed that works with Online Turbo Tax and will give you a free online tax return next year.
http://quickbooks.intuit.com/self-employed

You need to report all your income even if you don't get a 1099Misc. You use your own records. You are considered self employed and have to fill out a schedule C for business income. You use your own name, address and ssn or business name and EIN if you have one. You should say you use the Cash Accounting Method and all income is At Risk.

After it asks if you received any 1099Misc it will ask if you had any income not reported on a 1099Misc. You should be keeping your own records. Just go through the interview and answer the questions. Then you will enter your expenses.

Self Employment tax (Scheduled SE) is automatically generated if a person has $400 or more of net profit from self-employment. You pay 15.3% SE tax on 92.35% of your Net Profit greater than $400. The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare. So you get social security credit for it when you retire. You do get to take off the 50% ER portion of the SE tax as an adjustment on 1040. The SE tax is already included in your tax due or reduced your refund. The SE tax is in addition to your regular income tax on the net profit.

Here is some IRS reading material……
IRS information on Self Employment
http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Self-Employed-Individuals-Tax-Center

Publication 334, Tax Guide for Small Business
http://www.irs.gov/pub/irs-pdf/p334.pdf

Publication 535 Business Expenses
http://www.irs.gov/pub/irs-pdf/p535.pdf

We do not know what your state laws are regarding who needs a license to be a personal trainer/assistant. 

There is no federal law that requires you to be licensed in order to claim expenses when you are an independent contractor.

 If you are self-employed you will be paying self-employment tax for Social Security and Medicare, as well as ordinary income tax (depending on how much you earned.)  

Your business expenses will be entered on your Schedule C.

https://ttlc.intuit.com/questions/2903027-how-do-i-report-income-from-self-employment

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c

https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct

https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs

If you are using online software you will need Self-Employed.  You can use any version of desktop software and the software will be able to do a schedule C.  Or if you qualify you might be able to use Free File--it does not become available until mid-January:

There is another full-featured free version of the software:

Try Free File: 

You qualify if your income was $39,000 or less, or $72,000 or less if active duty military, or if you qualify for Earned Income Credit

https://ttlc.intuit.com/questions/1900583-what-is-turbotax-free-file-program

• https://ttlc.intuit.com/questions/2026912-how-do-i-switch-to-turbotax-free-file-program

Or—-Use this IRS site for other ways to file for free

https://apps.irs.gov/app/freeFile/

For income taxes, you are required to report all your income, regardless of whether or not you have a license, or whether a license is even required.  You are expected to keep accurate business records of your income and expenses, even if you don't get tax paperwork from your clients.  Your report your income, deduct your ordinary and necessary expenses, and pay income tax and self-employment tax on your net profit.

If you also have a W-2 job, you still file just one tax return that reports all your income.  It will have a schedule C for the self-employment as well as including the W-2.

You said you have been "freelancing" since May but you started as a PA in September.  You need to determine if you have two different sources of business income that need to be reported on 2 different schedule Cs, or if you really just have one "business."  Basically, you can combine all your business activities on one schedule C if the activities and deductible expenses are similar.  If they are very different, you need 2 schedule Cs.

For example, someone who does carpentry and also prepares tax returns in season would need to file as two separate businesses.  Someone who drives for Uber, Lyft and Doordash can file as a single business, since the activities (ride share) are essentially similar.