Technically this shouldn't be allowed, but it is very unlikely that authorities will notice it, especially since the earnings are relatively low. In fact, it sounds like she is not transferring any funds from these earnings to you, which is the key aspect of this set-up that makes it unlikely for you to get in trouble. Bear in mind that your girlfriend will have to report this income when she files taxes.
It shouldn't be allowed because you are still doing the work, and it's as if you are employed by your girlfriend. Both of you might be breaking some rule (as she should technically declare herself as a business/employer), but I couldn't imagine someone to care enough to go after you (just like no-one goes after students who get compensated for baby-sitting or yard work, etc.)
F-1 students cannot earn any funds whatsoever (no freelancing, no online shops, no sale of any products through a retailer, even earning funds abroad while physically in the US is not permitted), unless you obtain CPT (Curriculum Practical Training) or OPT (Optional Practical Training).
Web development is a very marketable skill and my advice to you is to apply for Web/software development internships after your first year of studies in the US by getting the CPT authorization - this way you will earn a lot more money and you wouldn't be breaking any laws. If you are close to graduating, you may continue to earn from your projects under your own name when you receive the OPT authorization (see F-1 Students and Entrepreneurship on https://studyinthestates.dhs.gov/training-opportunities-in-the-united-states)
Finally, every school in the US has staff members who are specifically trained to guide international students, so you should check in with your school about your options.
Source: I've been an international student in the US for 8 years now and counting...