IMHO, it is, CURRENTLY, very difficult to impossible to get Amex to raise credit limits once a card is opened (unlike, says, Citi). This appears to be a policy change brought on by a not so long ago near death experience which Amex does not want to repeat.
I suspect this will change at some point in the future ... but, who knows.
Meanwhile, no real harm in trying to get them to raise your limit by calling. I believe the policy is that at least two months must have gone by from time of card issuing or time of last request to raise limit for the new request to be processed.
If you do request a raise, please report back and let us know what happened.