I'm 36+2 too!! Is this your first? It can take weeks or days for baby to become fully engaged so it's a bit of a how long is a piece of string question I'm afraid. I've been told my baby is 4/5ths engaged too but as it's my second that it could bob in and out of the pelvis. I haven't been much help sorry but good luck!
I had this from about 30-32 weeks, possibly earlier I've had it in all of my pregnancies and went onwards without complications. I found it occurred on long days out with the kids or if I did too much housework or took long walks. Sometimes I took a warm bath or just stopped to put my feet up and totally relax.