The squeak you hear is common. What has happened is the plastic bushings in your spring bolts have worn out.
To replace these, you will need to get the trailer jacked up and the axles supported to pull the spring bolts. Pull them one at a time, drop the spring, and then slide the old bushing out. I'd personally recommend greasing the new bushing on the inside and then slide it right into the spring. Slide it back up there and put the bolt back in. Make sure you seat the perforations on just below the bolt head.
This really is a pretty easy job to do yourself, but I know you have limited supplies and this does require a jack or two and a set of four jack stands.
You do have a couple options for doing this job. The new plastic bushings shouldn't cost you much more than $5 if that, but they will wear out in a couple years or a few thousand miles.
Dexter Axle offers a wet bolt upgrade which a few of us have done. I believe JohnB did a tutorial on how to do it. Basically the kit give you new bolts, nuts, and new bronze bushings instead of the plastic ones. The bolts are special in that they have a grease fitting on the head and holes on the bolt shaft to keep the bushing greased without having to pull it apart. That will cost you about $130:
However, Dexter still has a unique deal going on for a further upgrade. I did this to mine because I saw the sale and it really did make sense. I called Dexter to order it and the guy told me they made up too many of these kits and they just want to reduce their inventory now, so they dropped the price a lot. So for about $20 more you can get the Ez-Flex kit, which includes the complete wet bolt kit.
The Ez-Flex kit includes a unique replacement equalizer that contains a rubber thing and compresses when you go over bumps. I was surprised when I installed it because it really goes over a bumpy road much smoother now. It almost makes the axles independent of each other and they share the rubber thing to cushion the bump.
2007 T-286SR Cherry/Granola, #6236, original owner, current mileage: 9467.8 (as of 5/26/19)
1997 T-2653 Blue Denim, #5471
1979 12 1/2' MC, Beige & Avocado, #4639
Past Sunlines: '97 T-2653 #5089, '94 T-2251, '86 T-1550, '94 T-2363, '98 T-270SR