You can do whatever you want and shaving won't make any more hair grow back than was already there. But most people chose to either bleach the hair on their arms or wax them. As when you shave it cuts the hair off at an angle so when it grows back it will feel and look very stubbly. Which is really not a good look on your arms. I'd leave them alone unless they are very hairy indeed (compare with your firends - you'd be amazed how hair most people's arms are.) If you do decide to do something about it definitley start with bleaching.
There are very few people in this world who actually need to remove hair from their arms. We are mammals after all and as arm hair is generally fine, it's deemed 'acceptable' in this obsessively 'body hair-phobic' world! I have loads of arm hair, but it's pretty fine and light in colour and doesn't bother me at all.
If you do think your arm hair is too dark and/or thick, I would definitely recommend bleaching it before you go down the removal route. If you do want to remove it, shaving is the last thing you should do. Go visit a reputable salon and get their advice about waxing and other methods that may be available.
You can buy these little exfoliating pads called silky mits, they are ideal for your arms. You just rub them in circles on the hair that you want to remove and it comes off, so using these you can just make the hairs a bit finer instead of removing it completely.
My advice is dont shave your arms! Use bleach instead, the hairs can grow in a funny way, and its awful for your boyfriend if he runs his hand up your arm and you have stubble, not pleasant!
I am dark haired and have very hairy arms! I use hair removing cream to remove it - works like a charm and lasts longer than shaving.
Don't shave! Takes ages, you'll miss some, itchy regrowth and prickly regrowth!
Superdrug have really low cost hair removing cream for sensitive areas. Its takes just 10 mins. I get up 10 mins earlier one morning and put it on before my shower. Slather it on, go make some tea.
By the time you come back upstairs and get in the shower - hair gone!