Please help!

[Monkeyandbananas]

This isn't an aibu but I am posting for traffic.
So, we moved into our new home 3 weeks ago. I keep waking up in the morning with itchy red bites and my husband has one or two.
At first I thought it was mosquito bites but after recieving them for 3 weeks I have come to the conclusion it's something else. I cannot find any evidence of bedbugs or fleas, athough I have notices a couple of bugs around the windowsill. (rentokil wont come out without evidence). The previous owner had a cat so I am suspecting it might be fleas, the carpet is grim and needs to be replaced anyway.
I have a three week old baby here and I am tearing my hair out. Any advice/help would be greatly appreciated.
Also, sorry if the post is a bit garbled...v sleep deprived right now!!

Fleas or bedbugs are usually quite easy to spot if you have white sheets. Are you sure it’s not just a mozzie? I’ve seen a couple already.

Sounds like fleas.

Rentokill should come out if you have an infestation, or you can get stuff from the pet store.

Where are the bites? Years ago a boyfriend's sofa was flea ridden and I got bitten mostly around wrists and ankles. Flea spray worked to sort it.

Yes if it's fleas they will mostly bite ankles and lower legs. It's also the right time of year for dormant eggs to hatch. They can go years before hatching is triggered.
You can get stuff from any vets that is very effective at getting rid of them.

Wash everything really well and try something like these.

http://www.petsathome.com/webapp/wcs/stores/servlet/en/pets/beaphar-flea-fumigator-35g-(online-only)?utmsource=google&utmmmedium=cpc&utmcampaign=googleeshopping&cmmmc=GoogleeCPCPC--%20googleeshopping--googleeshopping&ita=1976&ito=googleshopping&CAWELAID=120267720000001899&cmmmmc=&ito=GAG44515172083&itc=GAC210995954840&itkw=nil&itaexid=&itawnw=search&itawmt=&itadvc=m&gclid=Cj0KCQjwtZzWBRD2ARIsAIPenY0ZzqMOp-o5H3FnOWSx0sDvjF2dllHRfIo7hrhJXgZw0I-fsR94xSoaAkF9EALw_wcB&gclsrc=aw.ds

Indesit spray from the vets in the carpet and mattress will sort out fleas. May have to do it a few times to zap new hatchings