First and foremost, I love my dog, but I'm just not doing the right thing.
He's a 4 month old beagle mix. For the longest time, he was peeing and pooing on his peewee pad, and then out of nowhere just began going all over the place.
We (my fiancé and I) want to walk him, but our vet consistently tells us to wait until he's received all his shots. And also, our apartment doesn't have enough room for a crate.
By the way, with the peeing, I only scold at him when I catch him in the act, and even then, before I get up, he will stare at me, as if saying "TRY IT BIG MAN, TRY IT" . Any thoughts, comments, suggestions?!

Hi,
I am not a Vet, just a many years dog lover and owner.
The key is persistence; but may not work too well unless you take him outside for some walks. Even though the Vet said don't take him outside, he is already 4 months old, and really does need to be walked.
Here is a link with some suggestions:

http://www.hilltopanimalhospital.com/housebreak2.htm
Look under "Steps in Housebreaking Puppies"

Not having enough room for a crate, while you are gone, is a big disadvantage. Also, scolding him doesn't work, as you have experienced. Whenever he goes somewhere besides his pad, then use some White Distilled Vinegar to wipe it up. That removes the smell, and hopefully, he won't go back there. Dogs will continue going to the smell where they last went, making it there "bathroom".
I do wish you the very best.

This is going to sound like a stupid question so I will apologize ahead of time, a few years back we lived in a very small house, I run a rescue, and thou it is mostly guinea pigs, I occasionally get other animals, I kept my crates in the attic, when I did not need them, but if I had to use them for a dog, I either kept it under the kitchen table, some times in the bathtub, when the dogs I fostered where not in it, when in use I would put them in the crate in the middle of the living room floor, is there no where in the house that you could stick it while not in use.


The right size cage is one in which your pet can lie down, turn around, and have three to four inches of extra head space when sitting or standing. While the right-sized cage may seem too confining or too small to you, it is not for your dog. Please read.
proper crate sizing

I am not going against your vet, but it is hard to house break a puppy with out taking the puppy out side, and as long as I have been around animals I have never had a vet tell me this. By 12 to 15 weeks your puppy should be up to date on all of his shots followed by a yearly booster, I may be wrong, but I do not think so, please read Vaccination Recommendations for Puppies