Your question contains a very delicate topic: plagiarism...! As you guess, that's not very ethical and safe to copy images online and modify them, to then use them for commercial projects. Especially if you are totally aware of what you're doing and know a license is easily available.
"Making changes" is quite a relative term. It would be hard to judge what you did exactly and if you made enough changes to make the original image unrecognizable just by using the details from your question.
Finally, we can't really give you precise advice unless we can at least see the before and after of the image you're talking about; plus it's legal advice that fall in a gray zone where there's no precise guidelines (eg. infringement). What can be done is at least tell you objectively if your logo looks plagiarized or not.
Some big clues to help you:
- If you put the original and modified versions next to each others, is
it easy for anyone to see the second image is built using the first
one? If yes, buy the license.
- Also, if you remove what you copied from the original image and
replace it by another custom design you did, will that logo still
work or do you absolutely need to use the original image to achieve a similar result? If it doesn't work, buy the license. If you can use any other graphic to replace the copied image then maybe you'll be fine. Note that I put the "maybe" in bold since you could still receive a cease and desist letter and there could still be infringement!
There's unfortunately no magical formula to this.
Finally, even if you do buy the license, make sure to read the terms.
Some licenses are not meant to be used on commercial projects as you want to use it for. In general, it's wiser and safer to build a logo from scratch and do some research to avoid any issue.