Honest advice? Wait it out. He'll be crawling in a couple of months, and then he won't want to be held as much. Do you have a baby carrier, like a sling or an Ergo?
First of all he is not spoiled rotten, he's just comfortable with being held. I do not believe in the letting baby cry it out thing.
I used to carry my daughter around the house in the baby carrier when I had to do things as this would relax her and hse has moved out of that stage.
My suggestion try putting him down in other areas of the house and put the dogs outside or in a room so you dont have to worry about him getting stepped on. Get on the floor with him and play so he can get used to it as he needs the tummy time anyway to practice crawling and exploring.
Above all this is nothing to blame yourself about, remember that babies come with their own disposition and personalities. It just may be his personality . It doesnt last forever
My son is 3 months old and I kind of have the same problem. My fault as well lol. I just keep putting him down. I let him fuss a lil' bit n then I will calm him n get him happy to put him down again and have found he is sitting to him self a lil' longer each time. he's starting to kinda play w things and wants to grab things so I set him up on his play yard w a bunch of different things to look at and try n grab. He also likes to kick things so I make sure thats thee as well. Just remember that they are only babies for so long and one da u will not be able to hold him and cuddle him so do enjoy it.
Awe don't worry you are not doomed to the life of a clingy child who can never leave the arms of mama lol. My daughter was very attached I also breastfed past 2 once they start crawling and walking they get some sence of independence that grows with age. My daughter is 2 years old she plays in her room alone alot we still cosleep and very close but she is not overly needy she will want to come up for hugs and kisses all day but does not expect to not leave my side. Enjoy the close bond you share and cherish it while you can ven as frustrating as it is sometimes! Use a baby carrier if possible it will be more cmfortable for you to have your arms free and a happy baby.