Is there a limit to how many new chemical elements we could discover/create?

More or less, yes. We don’t know exactly where that limit is, but we know we’re getting close to it.
By definition, in order for something to be considered an element, it must exist for long enough for an electron cloud to form around the nucleus (0.00000000000001 seconds).
We recently demonstrably produced and named element 118, which is ridiculously unstable. It lasts for so little time we can only detect it with incredibly advanced, expensive machinery. And, it lasted not much longer than cloud formation took.
Theories state that there will be an area of stability somewhere around 126 protons, so we can probably push to about 128-130. Another island of stability is predicted at about #164, but we don’t know for sure how much of an effect this would have either way since the repulsion within the nucleus would be immense at that point. 
There’s also the problem that electron behaviour breaks down at #137, since the velocity of certain electrons at that point would exceed the speed of light under current formulae, so you couldn’t have a neutral element form there anyway.

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