Don't listen when people say you need a minimum of 5 gallons/filter/heater/blah, blah, blah!!
If you can care for a smaller tank without a filter just fine and your Betta is happy, that's all that matter's! And well, yes, you do need a heater lol but filters are optional with them and smaller tanks. And for a 1.5 you should be doing at least twice weekly 100% changes, it will make the tank healthier. So if you do that, he can stay in the 1.5 just fine, unless you don't like it
Okay, so what it looks like to me is lymphocystis, here's a nice little link about it: http://www.fish-disease.net/diseases/lymphocystis.php
and this one: http://www.aquaticcommunity.com/dise...mphocystis.php
But anyway there is no cure for this, it is viral so it can infect other fish but looks like you don't have other's which is good. Best thing to do for him is to keep him as healthy as possible, so start doing those twice weekly changes and keep on feeding those Omega flakes although try to get the pellets if you can and that way you can feed both alternating to give a bit of variety. Betta's love variety
Make sure to keep him warm to, around 78-80 if you have a heater, that'd be best. But he should make it just fine, keeping him healthy is the key!
Also just be careful with those Freeze-dried stuff, they usually promote constipation which is no good so if you can, try not to feed it every week is all. if you want you can get (might be a little more gross) but frozen bloodworms or brine shrimp, brine shrimp might be a bit better. And then you can feed that twice a week or so and that would surely help him stay active and healthy. Mind you all frozen foods can be a bit messy so it's best if you feed them before a water change