Tendonitis has a very long healing period.
I can attest to that. When I was 18, I had tendonitis in my elbow ("tennis elbow") from poor throwing mechanics in baseball. My elbow would feel like it was on fire and hurt so much I could barely throw from third base to first base without pain - even a lob. It took 4 years to heal about 90% (it has never fully healed and still bothers me once in a great while). It took a while to get past the point where there was little to no pain because I used to work with my dad in construction, so I was always using my elbow somehow. But not using it the wrong way helped the healing process, but again, it hasn't fully healed, and may never heal because I did do quite a bit of damage to it.
Unless bowling is something that puts food on your table, it would be a wise decision to slow down quite a bit and see a doctor. No sense in "toughing it out" right now and potentially, down the road, not being able to enjoy it at all.
Shoot, I love to bowl, but if my back is stiff, or another part of my body hurting might cause further pain and more time off than need be (and even throw off my game), I lay out for however long it takes to heal. I learned that lesson when I broke my ankle.