What Makes A Good Logo
A good logo looks good on both a dark and light background. Your logo would probably only look good against a black background. A good logo is also simple, yet memorableas well as being easily recreated. Just take a look at these text logos to see what I mean:
You had the right idea with your colour choice for that type of business (pink to represent femininity and yellow to represent youth), although the execution was poor. Aside from your logo looking like an Apple product with that lower case "i", I've also seen that little "eyebrow" design on many other logos before.
I felt the font choice wasn't very good, either; it's too plain for a business that focuses on beauty. Try picking a different font and stylising it a little (for example, you could turn the "O" in "Brow" into an eyeball and place an eyebrow over that).
We all had to start somewhere, so good job on your first attempt!
By the way, have more confidence in your work. Calling it "my first
little logo" alludes to me that you know the logo is abysmal and makes me think you don't have much confidence in your work. If you aren't confident in your "art", then what you design is going to reflect this.