Gene has you covered, but I thought I'd add a few data points to consider.
While your fill water of CH150 is lower than the pool, that won't help your pool's rising CH, it is causing it. As your water evaporates, it doesn't take the CH with it, it leaves it behind. When your auto-filler kicks in, it's just adding even more CH, even though it's a lower CH than your pool's. It's just going to keep collecting.
The only way to bring down CH is to do a water exchange. And keep in mind, when you fill the water back up, you'll be adding water that already has CH150 in it! Which means you'll have to exchange all that much more to get to your target CH. I did a small exchange last year, and filled the pool back up using water from my softener. So I didn't have to exchange much, because my fill water was CH-ZERO! I had to do that exchange because, even with a softener, the CH crept back up slowly. It took over five years, so I consider that a success. But instead of waiting another five years, I'm going to do a much smaller exchange each Spring. It'll be easier, and that'll keep my CH very close to target level constantly (as opposed to letting it get too far out of range).
I also don't like to let water out of my pool. It's risky (very small risk), but with these annual mini-exchanges done with CH-ZERO water, the risk is all but eliminated.
I get that a water softener is not in the budget right now, but consider this. You'll be fighting CH until you get one. Every day you wait is just that much more water you'll need to exchange (is water expensive in your area?). Which is money you could allocate to the softener purchase.
You can purchase a softener at Lowes for about $500. I bought mine from Lowes for about $600, and it's now about $750 (Whirlpool). It's going on 10 years old and still going strong. Not only does it take care of my pool's CH issue, it's quite luxurious in the shower. My toilets are not getting all "CH'd," neither are any of my plumbing fixtures, appliances, tile surfaces, shower glass, etc, etc. My investment has more than paid for itself just in terms of pool water maintenance, but is also returning huge dividends in prolonging the lives of all my plumbing, appliances and glass and tile surfaces. The longer you wait to "afford" a softener, the more it'll cost you in the damage your water supply is doing to your pool and house.
When I bought this house, the pool, the shower, the toilets were all trashed with CH build up. I had to replace the pool finish and I spent days scrubbing CH off of glass and tile and ceramic. Now, nine years later, all my fixtures and the pool are pristine, thanks to the softener. And by the way (I hate to admit), I never brush my pool. Not a trace of CH anywhere under water to be found! How's that sound?! I can't imagine having to brush my pool everyday. Yikes.
Do you know if your house is plumbed for soft water? You'd see capped pipes stubbed out in a wall somewhere, usually in the garage. If so, the installation is pretty simple. So your only expense would be the softener itself.
I did mine, EZPZ. I then plumbed my softener to my pool's auto leveler. That was more involved, but it was all DIY. Myself and others here would help walk you through everything, so you've got that resource at your back.
The SWG, Gene pointed out, will pay for itself in short order, but of the two, it is the considerably more expensive initial outlay. I'd get the softener first.
OK, so all that said, consider your finish's warranty when deciding on your target levels for your pool. CSI is the critical factor to keep under control, exactly as Gene advises. But the trick is to get your CSI in range while also maintaining your finish's warranty. Should you have a problem with the finish, the first thing the warranty facilitator will want to know is a history of your water chemistry. If you can't prove that you've been in their recommended ranges the entire time, (CH450 is not that!), they might try to negate your warranty. Even if you can site TFP's methodology as being better for your finish, they'll still have grounds to get out of any warranty repair. Think that through as you strategize your water maintenance goals.
Anywho, I do go on, but I really can't say enough good things about my softener! It was a great investment. The sooner you buy one, the better the return.