Can HPT Give False Readings?

Okay here it goes ive been having alot of sex lately with my husband due to me leaving i left on the the 16th of feburary so for the few weeks before that we were having alot of intercourse. Few days before i left i kept having sharp pains, but brushed them off so went on my vacation n few days n kept having them every so often. So my husband said take p.t. so now its been a week that ive been having these weird abdominal pains they only last for a minute or so but they hurt. So its now the 22nd off feb. N i took a pt test n it was negative. So i was relieved but pain was still coming every few days. So now its the 4th of march and im finally home n had sex again even though the pain was there few hours after sex i had a dream that i was pregnant. So i instantly took a test n its positive but to nyself im thinking maybe THE cum was giving it a false reading! Can the sperm give false readings? So i take shower n clean it all away n douche n wait few hours n take another one n the positivesign came up fast!! So after this long story is it possible im rreally pregnant or is the sperm give the false readings?? Please and thank for reading this and taking the time to answer -Catrina