I have expereinced exactly the same sound and I too thought I was hearing my heart beat. Mine is only in the right ear too.
Sadly mine is a type of tinnitus, it gets louder with stress.
It is of course very possible you only hear the sound because your ear need syringing.
Like yours mine at first italso sounded like water running under pressure if I put a finger in my ear. I saw an ENTconsultant who performed an in depth test and he confirmed it is a type of tinnitus. Fortunately it does not affect my hearing at all nor sleeping and is fairly mild. If you have got what I have got one gets used to it and hardly notices it after a while. The only thing that makes mine louder is stress. I try and ignore it and am not constantly aware of it. I am very careful with noise though. If you are a pilot never do the walk around without ear protection, the APU noise or passing aircraft nearby could make it worse.
I have been told by my consultant it might eventually go away or could get worse if I am exposed to loud sounds.
I am almost 51 and have had the problem for 6 years.
Tinnitus is not always the ringing hissing sound, some people hear, some tinnitus sounds like machinery or even music.
I have been flying for almost 30 years but do not hear it when flying or driving a car, the external sounds inside both an aircraft or a car drown the sound. I have not suffered any hearing loss at all. My last test revealed my hearing was above average for my age.
Best of luck I hope a syringe-out gets ride of the sound, it might go anyway in time.
I hope your's is only wax building up.