I have decades of experience with constipation (beginning as a baby) and no sign of diverticula. I wouldn't really consider that straining a little over four episodes would have caused it. The constipation is probably the symptom, not the cause.
For natural assistance, I recommend dried turkish apricots, dates and prunes, or even licorice and really increase your water intake as it will help get more fluid into the bowel and soften that stuff.
I'm not sure if I'm supposed to name things here or not, but after surgery in 2005 for ovarian cancer, I had a very sore and sleepy bowel and I was told about a concoction of herbs that acts as a lower bowel stimulant. It was extremely helpful in getting through the first weeks post-op and I keep some in the cupboard, just in case.
You can push a bit, but don't bear down like you're trying to give birth to a bowling ball. You're not, but honestly, after having a kid a couple of years back, the after effects from child birth felt like the muscles in my butt had dropped out. Couldn't walk properly for over a week. You do NOT want that result!
Push a little, ease off and try again. Just gently, so as not to strain too much, but get your body into the notion that things are on the move. You may have to grab a book and sit down and relax a little too.
As a former poster said, raising your feet or getting something you can lift your feet on to can help to reposition the body. Sitting on a toilet isn't the most ergonomic way to take a poop, but I'd rather sit than squat. Some people find visualizing helps to get things moving too.