I've heard or read it has risen for 1mm a year for many years.

It rises some places and it falls other places. For a variety of reasons.

Why does Sea Level change over time?

There are a number of factors that contribute to long and short-term variations in sea level. Short-term variations generally occur on a daily basis and include waves, tides, or specific flood events, such as those associated with a winter snow melt, or hurricane or other coastal storm. Long-term variations in sea level occur over various time scales, from monthly to several years, and may be repeatable cycles, gradual trends, or intermittent anomalies. Seasonal weather patterns, variations in the Earth's declination, changes in coastal and ocean circulation, anthropogenic influences (such as dredging), vertical land motion, and the El Niño Southern Oscillation are just a few of the many factors influencing changes in sea level over time. When estimating sea level trends, a minimum of 30 years of data are used in order to account for long-term sea level variations and reduce errors in computing sea level trends based on monthly mean sea level. Accounting for repeatable, predictable cycles, such as tidal, seasonal, and interannual variations allows computation of a more accurate long-term sea level trend.

Source:
https://tidesandcurrents.noaa.gov/sltrends/sltrends.html

Interesting map at the above site too.

I think tides and sea levels fall into much the same category as the weather and weather forecasts. There is much we know, but Earth is a big place with lots of variables, and our true grasp of geological time is also quite limited. Even though we know a hell of a lot about the weather, and forecasting is pretty good, forecasting the weather is still filled with a lot of speculation. The planet's weather still is a humongous, chaotic system controlled by an infinite number of variables. That alone makes it hard to nail things down. Meteorology and climatology are birds of a feather. Meteorology's short-term atmospheric conditions juxtaposed with climatology's rather long-term climate trends do not lend themselves to ironclad accurate predictions.