You need to dethatch and/or aerate. Aerating will do a good enough job. Rent one for the day since you don't have a tractor to pull a small one.
I would plan your own fertilizing for the year, Home Depot has Lesco stuff which is good (not as good as the professional grade stuff, but will get the job done) if you can't afford to have a professional do it.
Apply whatever you buy PROPERLY. Bad apps mean no results.
Also, mow high, it looks like tall fescue/rye grass, most people don't have the sense to mow it higher. Cutting your grass no less than 3.25 inches at the lowest will make a huge difference.