can sperm give you a false positive on an OPK?

Hi all
I'm in my second month of TTC for baby #2. 
I was just wondering whether or not sperm can give you a false positive and I'm second guessing why we weren't successful last month.
My cycle for the three months prior to starting was 25 days.
DH and I DTD every day from cd 9 until cd 19 - I got a nearly dark line on an OPK on cd 16 and on cd 17 when I tested with FMU just after DTD I got a positive on a digital OPK. 
My body started to show signs in TWW of pregnancy for eg increased sense of smell, twinges in lower abdomen and tingly sensation in breasts.
I got my period which was heavier and more painful than normal on CD 29.
I am second guessing whether or not I got a true positive on OPK as I have heard sperm contains FSH and LH (which is what the OPK tests for).
Thanks in advance for your help.