If you appeared before a court and
(a) pleaded guilty ; or
(b) were found guilty after a trial ;
you have a conviction and a criminal record.
Since you weren't fined (and you've not mentioned anything like community service), it seems reasonable to assume that you were either given an absolute discharge or a conditional discharge. In which case your conviction will have become 'spent' after 6 months (for an absolute discharge) or 12 months (for a conditional discharge, unless the period of the conditional discharge was longer, in which case the conviction would be spent at the end of that period).
Once a conviction is spent you don't have to declare it when applying for employment (unless the type of employment is exempted from the provisions of the Rehabilitation of Offenders Act - such as working with or alongside children or vulnerable adults) or for such things as applying for insurance. (Even if you're asked a direct question such as "Have you ever been convicted . . .?", you can lawfully lie and answer 'No').
At present all convictions (including spent convictions) will always show up whenever an employer (or other organisation) calls for a CRB check (at both 'standard' and 'enhanced' levels). That's clearly against the spirit of the Rehabilitation of Offenders Act, so the CRB is working on the introduction of a 'basic' level CRB check which won't show spent convictions.
Individuals can't get their own CRB check. The only way that you can see what is on your 'record' is to apply to your local police force for a copy of what they've got on file about you. You have a legal right to demand that information. There's a �10 fee; the police have up to 40 days to respond to your request.
To find out how to get hold of your 'police record', google this line:
"subject access" xxxxxxxx police
replacing xxxxxxxx with the name of your local