Personally, I would keep going, as long as symptoms are bearable.
It’s almost certainly colchicine causing gastric problems. But Coxflam (AKA Mobic) can also cause issues for some people. It’s an anti-inflammatory, meloxicam. In the UK, anti-inflammatories are often prescribed with other drugs that help reduce gastric problems. There are lots of options, but no alternatives to colchicine. If you really can’t tolerate the colchicine, many gout patients manage without it. That’s especially true when anti-inflammatory is supported with a pain-blocker such as paracetamol.
Finally, some people are affected by when they take medicines in relation to meals. Medication before, during, or after meals can make a difference. Your doctor or pharmacist should have advice on which might produce best results for different drugs.