Its up to you which course of advice you take, ultimately, you can get as many opinions as you like at this forum, but the final decision is yours, remember, no one here at this forum is an immigration solicitor, I suggest you pick out the best ingredients and follow your own gut instincts on this one.
Of course you have the right to have your case looked at again, you must go to the embassy and request at the reception for the entry clearance section that the entry clearance manager looks at your case, you have a right to ask for this within 48 hours of a refusal.
If the entry clearance manager looks at your case and then decides to uphold the decision of the entry clearance officer, then you are left with only 1 approach, and that is to file your appeal within 28 days of receiving a notice of refusal.
But I would caution you, to launch your appeal in the UK, and not via the British Embassy, it takes longer for them to send the paperwork through, whereas in UK it has been known to be quicker, you can get in touch with the AIAT at Feltham, and request the paperwork to submit an appeal for consideration in the UK.
The choices are of course yours.