No you are not compelled to contract with an insurance company. Being compelled to purchase would have fell under the Commerce Clause and would have been unConstitutional, to which Nasty Peelosi and Dingy Hairy failed to notice when rushing the Bill through Congress.
It is so arranged that if you decide to not purchase insurance the IRS can fine you a percentage of your gross income for having no specified adequate insurance coverage.
It’s not a fine, it’s a tax. Upon you contracting with an insurance company payment of the tax is waived. That’s compulsion.
The force of government action against you is a uniquely persuasive pressure to contract.