Perhaps one of the reasons you don’t have a pet is because you don’t want fleas in the house, but something that is important to remember is the fact that you can bring fleas (and have an infestation) without owning a pet. Sorry to be the bearer of bad news, but this is certainly a truth you have to accept. 

Fleas, during the summer months, can live comfortably outside on your property, so disregard the myth you heard about them not being able to live outside. Fleas can get transported into your home by hitching a ride on your trouser leg, sock, shoe, etc. Then, once you get inside, they’ll just drop off onto the floor and make a home in your carpet and other fabrics.
Fleas can also get into your home if you bring home something that is infested with them (furniture, etc). That’s why you have to be very careful with the things that you bring into your home and make sure that they come from sources that are not infested themselves. 
If you go to a location (commercial or private) that is infested, you can bet that pests will hitch a ride with you and find a new home to infest and enjoy, much to your disgust.
Lastly, by the time you notice fleas (whether they’re jumping around, or you see their droppings), the infestation has already been in your home for weeks or even a month. As such, when you are going through the timeline to try and find the source of your infestation, make sure you focus on the things that you brought into the house about a month previously. 
A flea infestation is serious because fleas can carry human diseases and bacteria that impact everyone in the household, not to mention the fact that you have a parasite living in your midst. So, while it’s easy to blame the “pet problem” in terms of bringing fleas into the home, you, yourself, could very easily be the carrier. So don’t kid yourself if you think you have fleas but don’t see how that is possible. It is easily possible and needs to be fixed as soon as possible.