Well there seems to be three issues here:
1) Irritation at your current job for changing your benefits package
2) You want to save "enough" for retirement
3) You want to still "enjoy your youth".
1. If your agreement with your current employer is in writing that he will always pay 1/2 of your healthcare plan premiums, and he is no longer, or doesn't want to start since it looks like you are just now going onto the "company" plan, sounds like breach of contract and you might have a case against him. Might not be worth much other than chest-thumping rights and legal fees. From a cost point, on top of payroll taxes and compliance related stuff, national average, your employer is playing about 30% additional for you, on top of your salary. So say that the company is "up 30% from last year" but what does the company expenses look like? Guy might have promised you something he can't deliver now because a change in business environment, or because he is trying to stiff you. You can either trust him (which your OP suggests you don't) and keep working in a fairly good starting position, or try to find something else.
2. "enough" for retirement is entirely subjective. You'll need to answer for yourself several things, including how long do you expect to live, how long you want to work, what kind of income to you expect to need in retirement and what extras you want in retirement. These does not even count family needs between now and then either. Your choice on married or kids but those will need to be factored in, at the very least a firm negative or open to the possibility. Once those questions are answered then you should go to a financial advisor. My bank has one on staff, open to free consultations, so who ever you bank with should as well. At age 23 though you have tons of time to plan for retirement. If you work to full retirement age according to social security(68 and a few months I think for you) that gives you a good 45 years to prepare, potentially, if not longer if you choose to continue to work.
3. Enjoying your youth depends on what you enjoy. Do you want to buy a book a month or do you want to drop a grand a month at a club (extremes I know). This just takes budgeting though. There are a bunch of different monthly budget plans put out by multiple groups. I suggest you find one and adjust it to your needs. I prefer a "Needs, Wants, Desires" plan. Fund all the needs, As many wants as possible, and if anything is left over prioritize your Desires and get those also, without sacrificing your Needs and Wants.
Needs: Food, Housing, Communications, Transportation. Wants: Better communications, community contributions, better/more food, house hold conveniences, pets. Desires: Entertainment, eating out, planned moderate expense family get-togethers, vacations and savings for high dollar non-mandatory household expenses.
Example of high dollar non-mandatory expense. Planning on upgrading our water heater to an inline tank-less variety, electrician, unit and installation should be around $1800 and change for the one I want.
You seem like you're on a good path though.