if you are only able to use one hand whilst pumping you are inevitably going to cause damage using a frame pump. a foot-pump or floor pump would be a much better option which can be used with one hand and not put pressure on the valve.

http://http://www.walmart.com/ip/Floor-Pump/11065181?findingMethod=rr

another method would be to use a gas pump (but make sure that you always carry spare containers) although more expensive to use.

also you really need to try to become self sufficient by repairing your own punctures, i know this is more difficult for you due to being less able, but because of this you rely on your trike more than fully able bodied people!