It sounds like you need your very own wetsuit, preferably one that is made for cold waters. Not sure if you can be too warm in a wetsuit, honestly, I am not an expert in this, but you definitely need a warmer one than an average person in a particular water temperature. And if you rent a wetsuit from a diving school, you get whatever they have available. You might try asking whether they have warmer suits, but I think in general, especially in tropical countries, they will not have much variety.
Another problem with wetsuits is that they have to fit you perfectly. It should be difficult (yet possible) to put it on/ take it off, and it should be as tight as possible. Because if there is any space for water/air in between the wetsuit and your body, you will be cold. I myself am tall, and when renting wetsuits in Asia I was constantly given ones that were way too big for me widthwise.
In case you decide to buy a wetsuit, you could check out this for choosing the correct thickness: https://www.evo.com/guides/wetsuit-thickness-and-temperature-chartWetsuit Thickness Guide & Temperature Chart.
And this video for getting the correct size: https://www.youtube.com/watch?v=MNv3vmfFwwgFinding the Right Fit (Youtube).