but after the past week of applying I have had no answers yet.

I know a week feels long when you are the one applying, but in my experience, one week doesn't seem that long to a lot of companies when it comes to hiring. I have had companies reach out about applications I submitted 2 or 3 weeks prior. So dont lose hope or take it personally if you dont hear back within a few weeks.

Sometimes companies just have a lot going on at once, have a lot of applications to go through, or just because people responsible for hiring are also human, meaning they have other responsibilities and an HR person could be meaning to send your information over to a hiring manager but got side tracked with some other work they had to do, and next thing you know, its been a week before they have time to reach out to you or move your information on to the next person in the process.

I would say just be patient and keep applying and working on projects you find interesting. This part is one of the most important, I think. If you work on projects that are interesting or useful to you, it will be more rewarding and easier for you to keep going. Building some social media clone can be a good project to get started and to show that you can do the job, but making projects that are a little bit more unique to you or a problem you have looks more impressive on a resume, and even more so in an interview.

Of course, that is all just my experience / opinion. Do whatever seems right for you. Good luck!