Hi chocwocdoodah I had this exact sensation 18 months ago. Mine was confined to my left breast and was accompanied with pain radiating from my underarm into my breast. I distinctly remember thinking "gosh I feel like I might start lactating" even though i'd finished breastfeeding my 3rd baby 2 years previous. I also remember a pressure sensation, as though something was pressing from behind my nipple.
My GP referred me to the breast clinic and they did a thorough examination & ultrasound (too young for mammogram apparently at 36). Nothing untoward was found, I was told to take high strength evening primrose oil and eventually all faded away (plus I stopped carrying my far-too-large 3 year old on my hip, which I think is what caused the underarm / boob pain!)
My left breast does seem to be my 'naughty' breast - I suffered mastitis that side, it always massively overproduced milk and was also my 'favourite' breast to feed from as it never seemed to run out of milk. I was told at the breast clinic that it is a very dense and fibrous breast, as observed from the ultrasound.
Funnily enough, its misbehaving again and i'm waiting for another breast clinic appt to come through as I was referred again this week by the GP - same left breast, stabbing pains from behind nipple. He said the breast tissue all felt fine when he examined me, no lumps etc. However, I have since prodded and poked that poor boob so much that I can feel a lumpy area and possibly a small lump (which is totally unpalpable using the normal self exam techniques - I have to squeeze firmly to feel it) in the left breast, so I'm glad that I pushed for a referral.
Definitely see your GP - more for your own peace of mind. I tend to find that symptoms get worse and worse the more you worry, then once someone properly placed has told you there is nothing to worry about, symptoms tend to sod-off fairly quickly!