I just started back up on the violin. Last time I played was 15 years ago when I was just a kid. I can't afford both the violin AND a tutor, so I'm relearning on my own for now.

My fingers are considerably larger now, and I am having difficulty keeping my fingers from touching other strings. While holding down the D string, my fingers are touching the A string, causing nothing but issues. I can sometimes get them to separate when playing pizzicato, but not always, and not at all when using the bow.

Is this something I am going to have to endure until my fingers callous over?

I am hellbent on relearning, so if there are any tips on how to overcome this, I would very much appreciate it.

I am afraid it's the dreaded P word (practice). Generally, if you are playing on 1 string, it doesn't matter if you touch an unplayed string and in any case can compensate by moving the finger across the string. It all comes with practice. The other thing that you may want to check is the action (height of strings above the finger board) often new instruments set the action way to high.

And I thought I was the only one with FAT fingers. Some times I adjust my finger so that the other string it touches is one that either isn't being played or where it touches is below where the other string is fingered. I can clearly finger two strings with one finger, and some times when fiddling this is a help. Like the other fellow said, practice. I have played over 800 hours this last year, and at least another 400 hours on the mandolin, and I still don't have any calluses on my finger tips! And now I've started playing banjo too, but only learning the rolls now. What kind of strings does your violin have? Even the first cheap set that came on my violin didn't bother my fingers. Maybe your strings are way too high of the finger board?

I can't really do any modifications to it (aka changing strings and such), because it is a rental. We are trying to save up for a move, so we couldn't justify outright buying one right now.

That's even better. Take it back to where you rented from and let them know the strings are hurting your fingers. They can check if they are too high off the finger board, and maybe even up grade the strings while they are at it. And it should be at no cost to you, since it is their violin.
Nylon (perlon) strings are wrapped too, so they will look and feel just like steel strings. Like I said, even the cheap steel strings that came on my violin never hurt my fingers. Fat fingers at first is an additional challenge, but it can be a plus later when you start playing a lot of double stops.

Bring your left elbow in towards the bottom of your breastbone, so your palm is parallel to the neck, or as close as you can get it anyway. It will feel un-natural.

This means that you should be looking at the sides of your fingers, instead of the fingernails when you look down the neck (or as close as you can come to it).

Doing that will position the wide edge of your fingertip along the length of the string, instead of across two of them.

Also, keep your wrist straight as you can, making sure that your left palm stays away from the neck, instead of "palming" it. That means you must really arch your fingers to get them down on the strings.

When you fingers are arched enough to press on the strings with the very end of your fingertips, that will also lessen the tendency to touch adjacent strings.

Your intonation will also be better when you are used to doing these things.

As my teacher told when I first started, "Nothing You Do Will Feel Natural Or Comfortable".

Aside from that, play VERY slowly during practice to be sure your fingers are clearing the adjacent strings... practice slowly and often.

I can sometimes get them to separate when playing pizzicato

You really said it all right there... if you can ever get them to separate, you can always get them to separate, with enough slow practice at it.

"Enough" may mean "A LOT", but the keys are Slow, Careful, and Plenty.

Well... That used to happen with me too. I also thought it was because i have "fat fingers", but my teacher told me to practice SCALES and to focus on that. I have to say it worked.. But it wasn't the fact of just playing the scale.. is actually playing it right, with NO mistakes! In other words... Taking the time to play every note perfect!!

I used to have this problem too. My teacher told me to focus on the shape of the fingers. If you come to a note where you are having this problem look at the shape. Is your finger lying flat against the string and are you playing on the pads( Fingerprints) Of your fingers? Or are your fingers squared, and are you playing on the very tip top of your fingers? If you are playing flat , try playing on the tips of your fingers....Hope this helps