Is my pump faulty or my tyre? I have recently bought a Specialized women's road bike and for the last couple of weeks was borrowing my boyfriend's hand pump with no real issues. 

Last night I finally purchased my own (Topeak RaceRocket HP) but each time I try to inflate the tyre (just a top up of air, not from flat) I can either hear air hissing out (I believe the pump isn't screwed on enough then) but even a quarter of a turn too far means the pump won't work as the air pressure seems to be too much and this would suggest I've screwed it on too tight. Just can't seem to get a happy medium. 

It could be resolved with a floor pump but as I've just dropped £30 on this, I want to be sure before I spend another load of cash just to eliminate possibility.

Any suggestions? Should I return the pump or am I doing something wrong? 

Thanks :) x
As other have commented since you can fill the tires with another pump the issue is not your tires. If you bought it at your LBS (local bike shop) I would bring it in and have them demonstrate its' proper use. If they  can't get it to work they should replace it at no charge. While the listed capacity is 160psi, the amount of effort required to generate the pressure will vary with pump design. A larger diameter pump will require fewer pumps to inflate a tire but with more effort. While not as much of an issue with a floor pump the difference can be considerable with a small pocket pump.