2018 is my first year as an Independent Contractor (tattoo artist). Can I file my quarterly taxes now?

Unless you have W-2 employees, you don't "file" anything for quarterly taxes. You "pay" quarterly taxes. You can do so at <a rel="nofollow" target="_blank" href="http://www.irs.gov/payments">www.irs.gov/payments</a>.

The first year you don't need to pay estimates as long as you pay in (by withholding) as much as your tax was last year.  But if you will have a big income you should send in estimates so you don't owe too much next April on your tax return.

For SE self employment tax - if you have a net profit (after expenses) of $400 or more you will pay 15.3% SE Tax on 92.35% of your net profit in addition to your regular income tax on it. So if you have other income like W2 income your extra business income might put you into a higher tax bracket.

You must make quarterly estimated tax payments for the current tax year if both of the following apply:
- 1. You expect to owe at least $1,000 in tax for the current tax year, after subtracting your withholding and credits.
 
- 2. You expect your withholding and credits to be less than the smaller of:
    90% of the tax to be shown on your current year’s tax return, or
  100% of the tax shown on your prior year’s tax return. (Your prior year tax return must cover all 12 months).

Here are the blank Estimates and instructions…..
http://www.irs.gov/pub/irs-pdf/f1040es.pdf

The 1040ES quarterly estimates are due April 17, 2018, June 15, Sept 17 and Jan 15, 2019.  Your state will also have their own estimate forms.

Or you can pay directly on the IRS website https://www.irs.gov/payments
Be sure to pick the right kind of payment and year.....2018 Estimate