Is the US job market really doing so well right now?
Disclaimer: I'm not any authority on economics, but a few minutes searching yields some results that appear to show that the job market is doing well in general. However, your industry might be different.
Are the rejections because of my lack of experience?
This is hard to tell without more details, and it probably is not possible to know 100% regardless. There are so many variables that go into either a hire or a rejection. Sometimes there are just better candidates. I will say that it
can be harder to get some jobs without experience. It is a classic chicken versus the egg problem.
Every time I get rejected, I just can't help, but to look back at the job offer that I declined over two years ago.
My best advice on this is to not look back. We all have decisions that might not seem optimal in retrospective, but you had your reasons at the time.
What can you do to increase your odds?
No matter your industry, you can do personal projects, job shadow, network with people in your field, volunteer, tailor your resume, and probably most importantly practice interviewing as much as you can.
The amount of actual experience may not be as big of a deal as your ability to portray it as the right experience to fit an employer's needs. Any one of the things listed above could tip the scales in your favor.
Hope it helps!