It sounds like you have a Yanmar 1GM like me, or maybe 1GM10. My impeller fails just about every other year for no apparent reason. Like Benny said, look over the side to see if you are discharging the exhaust water. When you rev the engine, you should get a decent amount of water spitting out. If your impeller has failed, you won't get any water spitting out. BTW, I can never find anything wrong with the impellers when they fail. They look and feel exactly like a new one, but I replace it and it's good to go for another few years until it mysteriously fails again. Some folks replace theirs every year. I just wait for it to fail since there isn't any likelyhood that it will fail at the worst time (we don't have problems with tides, current or other problems like that)
If you have a partial clog, you may get a very weak water flow, but not enough flow to prevent the overheat alarm from going off. Don't worry when the alarm goes off, there won't be any immediate danger. Just don't continue to operate with the alarm sounding. Personally, I've never been able to detect any extra heat from the engine when the alarm goes off.
Keep in mind that you could have weeds clogging the hose between the intake and the strainer. I've been frustrated by that on one occasion when I cleared the intake and cleared the strainer and still had weak flow and the alarm go off.
If you don't have a strainer, then you may have to look at the hose from intake to water pump, but I would guess that you must have a strainer.