Your GP wasn't worried even though your pulse was 120?
How old are you? Are you on any meds? Do you eat/drink certain foods that contain caffeine or have certains ingredients which can cause your pulse and BP to go up? I for exampe cannot take Ibuprofen because my BP goes up, and I am on BP meds, doc said the BP still can go up in certain people when taking Ibuprofen despite the BP meds. I cannot drink Slim Fast, my pulse goes up and I get anxiety, the same with "Splenda". Yes, Splenda, google it, and you will find out what it can do to "certain" people for which I am one of them. Yet my BP meds and the Zocor I take give me absolutely NO side effects.
Get yourself a home BP monitor, and take your BP at least once a day, the BP monitor will also tell you how fast your pulse is. Or you can look at your watch and take it for 15 seconds and multiply it by four.
Sorry, you said that you took your BP at home. No need for me to advise you to buy one. :) Check it once a day for about two weeks. Write the numbers BP and pulse down and show them to your doctor the next time you see him/her.
But like I said make inventory of what you eat/drink, and what meds including over the counter you are taking, if you are taking any.