Pregnant and employed

So I’m just wondering how I can tell my employer that I’m pregnant. How did you do it? I am now 5 months, found out in May, started job in June, had a month break due to school being out and also wasn’t sure if the contract would be continued once school started so never informed employer. Contract continues and went back around the end of August so been back to work for about a month now. I am high risk (preeclampsia) I’m not due till Jan 20th but doctor wants me to have her about 37-38 weeks which is about the end of December beginning of January.

How can I tell my employer I’m pregnant? Would I tell him when I’m due as well? I know I should’ve told sooner but because of the uncertainties with their contract I never informed them. I’m just scared I’ll get discriminated against even though they can’t do that. Like cut my schedules or just not let me go into work. Any help would be appreciated.