I don't know what to do. Buy a dedicated camera or telescope to improve my actual equipment?

Of the two, the mini-scope will benefit you the most. I'd add a Nikon D5300 if you can find one used within your budget and maybe have it modified. If the D3300 is modified already then stick with it until funds will be enough to buy a dedicted cooled astro-camera. Don't waste your time/money with the ASI585.

You'll benefit from either one of these. I'm not sure which version is this 55-300 lens but upgrading to a triplet refractor telescope will change the game.

As everyone has pointed out, given the options you are looking at, the scope makes the most sense. 

From your question and from your profile, I see that you are using the DSLR on a star tracker mount without a scope (just the Nikkor AF-S DX 55-300mm f/4.5-5.6G ED VR zoom lens).  If you get the camera, what would you attach it to?  Although it is technically possible to attach a ZWO camera to a DSLR lens if you can find the right adapter, the result will likely be hard to use (you'll need some way to attach it to the mount, and I suspect focusing will be difficult). 

The 61EDPH II f/5.5 Triplet APO Refractor + flattener/reducer will run upwards of $700 here in the US.  You could pick up a ZWO ASI183MC Pro Cooled Color for just a little more than that, but without a scope, what would you do with it? 

Depending on your commitment to the hobby, it's good to have a plan for gradual upgrades as you can save up more money.  From your gallery, it seems like you have caught the fever, so I suspect you will want to keep investing in the hobby!  As others have pointed out, you will eventually want a cooled dedicated astro camera if you want to take your imaging to the next level, so it doesn't really make sense to spend money on an inferior camera right now.  Unless you are exclusively interested in wide field imaging, the other thing you will eventually need/want is a better equatorial mount with go-to capabilities.  If you were here in the US, I'd suggest that you consider buying used (CN, Astromart, ebay) – sometimes you can find good deals for entry-level stuff – but I don't know how available used equipment is in Chile, or if that's an option at all.  

Good luck and clear skies! (Sorry to hear that you are in Chile but in a bortle 7.5 zone!  At least you don't have to go too far I guess for some seriously clear skies!)

Well I would go the 533. To be honest people think a triplet is going to perform better than a doublet. But the reality is both perform well if you know how to pair them with the right cam. The 533 um pixel size with ed72 will work if you drizzle. True you will get tighter stars with triplet but you'll need to track and guide just the same or they will blow out and you'll struggle to see the difference. A 533 cooled is going to give you a whole new perspective on asyrophotography as it will look and feel different to a dslr. I would master that first and then upgrade my scope later.

Coolhandjo:
Well I would go the 533. To be honest people think a triplet is going to perform better than a doublet. But the reality is both perform well if you know how to pair them with the right cam. The 533 um pixel size with ed72 will work if you drizzle. True you will get tighter stars with triplet but you'll need to track and guide just the same or they will blow out and you'll struggle to see the difference. A 533 cooled is going to give you a whole new perspective on asyrophotography as it will look and feel different to a dslr. I would master that first and then upgrade my scope later.

I don't think the doublet and the triplet should have the same level of performance when using color cameras. In my experience the doublet even apo doublet gave me slightly more bloated stars when compared to the triplet, same with color correction - the triplet gave me better results. 
I think he can get away with the DSLR but for now should have better optics and mechanics. I know how crazy it is to go from a DSLR to a coolled camera specially on a hot climate but that will happen eventually.

If I were to pick between the two, I'd go for your scope first, especially with a good reducer.  You're going to be quickly pushing the limits of your star adventurer, weight capacity and tracking accuracy.

I will echo Marcelof's comment about getting a mount.   I would start saving now.   The mount is the number one key to success in this hobby.  Without a good one, you wont go far.      I will also say, this hobby is not cheap, at all.  I started in roughly August of last year…. I thought I was gonna be like you, slowly upgrade as I go.  I realized very quickly the limitations of this 'cheaper' equipment that I started out with.    You get what you pay for.   I ended up going ham and purchased a full AP setup with no holds barred.

Get the Sharpstar if you want it…   make sure you get a reducer.  

Next step is I would save for a mount.  Skywatcher mounts are a pretty popular go to.  Things like EQM-35 and EQ6R Pro are the most popular ones.   

From there work on your dedicated camera.     Don't get the 585.    As cool as it sounds, it's not a deep space camera.    You make not understand this now, but you will later.  Trust us.    I would suggest a 533 camera….and I would also highly suggest you go mono.   If you plan on imaging from your bortle 7 zone, you won't go far with color.    You could also consider a 294M, many folks are offloading these cameras right now as they're upgrading, but it's really not a bad camera.    

There are other pieces to go along with this equation like a guide camera, guide scope, filters, etc…  they easily add up the cost too, so don't forget them.


If these prices are out of your range, stay wide field.    Stick with your sharpstar, save up for the camera, and later on down the road you can look into a real mount.    The longer your focal range gets, the more exponential the cost becomes.