I may be an outlier here, but stretching aggravates my lower back. I have a little bit of a scoliosis type thing though.

What I find works for me is back strengthening exercises. Low weight and high reps. I never have back problems when I'm doing that consistently.

Honeslty - see a doctor.

The advice peole are offering here will either help or do nothing or make your problem worse and if you try all of them - chances are pretty high you'll stumble across one that will make it worse.

Your pain is a symptom, not a problem. You need to find out what the problem is before you can fix it.

will be sleeping on my side to relieve pressure on it tonight

In this position it helps to additionally put a pillow between your knees to keep your legs aligned (and thus prevent lower back from being tweaked toward your sides).

Sitting yoga, talking a walk, lying flat on the ground and not a mattress for a while, changing seating position often, getting a better chair, static stretching, light aerobics, swimming.

I've been a fellow sufferer of lower back pain myself.
Try this.

A back doctor taught me the technique, but I found this YouTube channel that has the same style of stretching.

EDIT: Also, I think you're supposed to apply heat, not cold, to a muscle spasm.
Try applying heat for five-ten minutes, then lay on the floor and do the stretch.

I'm sorry you are in pain. I've been there, and I know how terrible it can be.

Every case is different, so it's best if you see a doctor. I'm in a country with good, socialized healthcare, so it was much easier for me than it is for most of people. I've seen a specialist several times, had two MRIs and 3 rounds of physiotherapy in the span of 6 months. Here are things that worked for me:

• take NSAIDs, when they kick in, start with simple, not strenuous exercise. Check YouTube for back pain exercises. Some of them worked wonders alleviating pain almost instantly. Other ones helped to build muscles needed to support the spine, so I'd do them too. Do what you can, if it's too much, try another time. Repeat every day, even 5 minutes a day can make a huge difference. Walks are great too. Move as much as possible without exerting yourself or making the pain worse.

• get comfortable shoes. Flat, flexible sole worked great for me (I like Vivobarefoot shoes). Walk in these.

• red light therapy helped me. Lamps are affordable, easily available online.

• if you sit down for work, try to get a high quality chair. I've been sitting for years on a bad IKEA office chair, which made the problem worse. Once I switched I couldn't belive how much difference that makes. Standing desk is nice too, but not a game changer for me.

• As the pain got better and better I've been introducing more movement. I need regular exercise to keep my back pain free. I've actually started enjoying my workouts and a mix of strength and HIIT cardio exercises works best for me.

I hope my advice will also work in your case, I wish you all the best.