When calculating a confidence interval for a proportion, you should keep the following in mind:

In practice, we may trust this confidence interval when the number of successes is 15 or greater and
the number of failures is 15 or greater. That is,
when $np_0 \geq 15$ and $n(1 - p_0) \geq 15$.

The confidence levels can be very inaccurate unless your sample size sample is large.
The actual confidence level is can be less than the confidence level you specify.

This website also computes the "plus four" interval.
Statistical literature suggests that the plus four interval yields better results
than the usual large-sample interval.
Experts in statistical practice recommend that you use the
plus four interval for estimating a proportion when
the confidence level at least 90% and the sample size is at least 10.