The following does not constitute medical advice. However for general understanding only, deep veins, in this context, are those running though deep muscle in the arms and legs... (not fingers and toes) DVT's usually form in a limb, and result in that limb becoming slightly swollen, warmer than normal to touch, and rather red in colour. This is because blood is then diverted to the surface venous system which make the skin extra warm.
Generally speaking we are more worried about proximal clots than distal ones (that is to say those closer to the central trunk of the body than those nearer the hands and feet) because the veins are larger the closer you get to your trunk and a large clot, if it dislodged, could then embolise in the lung causing a PE - which is a life threatening emergency.
However a small clot in the finger would almost certainly not be large enough for such a concern, except in so far that it might be an indicator that you blood cehmistry was less than ideal. In many cases clots in distal venous systems are left to resolve naturaly.
While what you describe does not sound like a DVT, you should certainly still get it checked when convenient just to be safe. Also if it were a small clot then because of the distal location, it quite likely that all that would be required was some adjustment to your blood chemistry to increase your INR.
Unfortunately proper DVT's generally are considered a major contraindication to HRT, but as a real DVT could become fatal, that fear is absolutely not a valid reason to avoid getting checked over if you are worried.
I would also add that if your finger is numb, tingling or cold to touch you should get it checked immediately because complete failure of circulation in a digit could in theory lead to ischemia and amputation. Bottom line if you are worried get it checked.
