Just a few months ago the Supreme Court in 'Wayfair' allowed states to require you to collect and pay sales tax on actual sales, and many are moving to do so, although AFAIK so far most are only doing so for business volumes above some threshold -- and although you didn't say your size most single-person businesses are pretty small. See e.g. https://www.nolo.com/legal-encyclopedia/50-state-guide-internet-sales-tax-laws.html .
If 'affiliate' means you aren't actually selling the goods or services, just getting paid for a reference or facilitation, that should not be subject to sales tax AFAIK.
To be clear, as a sole proprietor (including a disregarded single-member LLC) you must generally pay income tax and self-employment tax = Social Security and Medicare equivalent to 'FICA' taxes on W-2 employees. To be exact, your business income on Schedule C (or possibly C-EZ, if the Trump 'improvements' haven't eliminated it like they did 1040A and 1040EZ) is subject to self-employment tax on Schedule SE; your business income plus any other taxable income, less deductions (including a deduction for half your SE tax), and starting this year for nearly all small businesses (again assuming you're small) less a 20% deduction for 'Qualified Business Income', is subject to income tax.
Also since you're new in case you don't know, you probably need to make estimated payments. In general 90% of your Federal taxes must be paid during the year, not waiting until next April 15. For payroll employees normally withholding covers this requirement, but if you are making nonnegligible income from nonwithheld sources -- including self-employment and also investments and some other things -- you need to either make estimated payments or if you have withheld income as well (i.e. this business is 'on the side') you can request extra withholding on W-4. The exact rules are pretty complicated, and there is a 'safe haven' that will usually save you from the penalty if you mess up the first year you have new income only; either see the IRS website or ask a more specific Q after checking existing ones. If your state has an income tax it usually has similar requirements.
If by 'new tax law' you mean the Tax Cut and Jobs Act last December, it does not affect sales taxes (which are not Federal), but does add the new QBI deduction for small passthroughs and reduces rates for C corporations (non-passthroughs). It also relaxes expensing and 'bonus' depreciation while (further) restricting deductions for meals and entertainment and some fringe benefits, both of which shouldn't affect an online-only business, and makes major changes to handling of foreign income which shouldn't affect you. And makes numerous changes that affect income tax payers regardless of business form, and are covered by plenty of other Qs.
