As you say, if it's raised, it's only by a little bit. If you have a family history of high BP/heart disease it's certainly good to be aware of that and to do what you can to keep it at an optimum level. Definitely add more fruit/veg into your diet and if at all possible follow a Mediterranean type diet with plenty fish, chicken, olive oil, nuts veg and fruits. And if you can include a bit more exercise - walking, taking the stairs wherever poss - that would be good.
Did you just take a one-off reading or a few? And when you took it had you been sitting down quietly for 5 mins before taking it? I think it might be an idea to take it at regular intervals over the next week and see what it's up to. First thing in the morning (laying down and then after you've been stood up for a while.) and if you are at home in the day, again around mid afternoon. And then before bed. Write the readings down so you can show your GP if necessary.
If you have no other symptoms I think I'd be tempted to keep monitoring it yourself for a month and making a few adjustments to your diet/exercise/salt levels etc. Then if it's still a little bit raised I'd discuss it with your GP. Also, if you are v worried about it, then don't wait for a month and go anyhow. Your GP will be able to advise and could arrange for a 24 hour monitor if he thinks that would be helpful.
I don't think you are being a hypochondriac one bit, esp as you have a family history of high BP and heart disease. It's much better to be aware of it. I had a scary pregnancy and ended up with pre-eclampsia and an emergency cs section because I had no idea I had mega high BP in my 20's. In my mid-20's it was around 150/120 and I was put on drugs straight away and have been on them ever since.