I have been doing training for 3 months with a trainer, however, I can no longer afford it, being a full time student. Now, to be honest, I also hate doing anything outside actually fighting or practicing fighting techniques. I was wondering, If I slowly go through my punching motions with heavy weights, will it increase my strength?
Doing slow punching motions with heavy weights will in first place train your musculus deltoideus
. So for that part you will increase your strentgh, but if your are asking about strentgh for fighting you will need more. For punching i.e. the whole body is involved beginning from a spring motion at your feet, hip/torso/shoulder rotation, arm extention. A good start for training the muscles needed are BWE like push ups, crunches, jumps. Then it will be useful to train with a heavy bag.
Also, not sure if it makes a difference but I always try to get in 2x10 push-ups a day (I know that's not a lot, but I'm 280lbs, but arms can't take much more than that.) And 4x25 sit-ups.
Sets of around 10 repetitions are usually done for hypertrophy
training, which to some extent you want to have, but what you want to have even more in combat sports is muscular endurance which you train with more repetitions (>20). You could do your push ups for example on an inclined surface or with your hands on higher ground (i.e. on two chairs, doing the push ups between them)
Lastly, Anyone know of a good way to self train for BJJ?
No, there isn't. It's that simple. Anyone who tells you otherwise is fooling you. Forget instruction DVDs. If you don't have already more than just basic knowledge you can't reasonably train on your own. You will get accustomed to mistakes which are hard to get rid of later if you don't have anyone who controls you.
I was looking at gyms, but I can't afford the crazy prices (the cheapest one within 20 miles of me is $180 a month).
$180/m the cheapest┐ Either they are ridiculously good or ridiculously expensive.