It is absolutely possible for you to move to the US; you need an H1B (Persons in Specialty Occupation) visa, or some equivalent working visa to be able to do so. The US department of state has a good summary of how you might qualify online.
Your options are absolutely not limited to just large companies; I came to the US and joined a ~ 20 person startup. You just need a company willing to do the paperwork to get the visa approved, and the ability to get appropriate wavers for hiring foreign workers rather than local workers. For IT, that is reasonably simple - though a larger company can obviously better afford the costs.
You might find the L (Intracompany Transferees) visa another useful path; if you work for someone who has a US office, you can transfer through them without the same degree of competition as the H1B.
Self employment, without a sponsor, is non-trivial, but it is possible. The simplest would be the E5 (Immigrant Investors) visa. If you have at least US $500,000 to invest in creating work in the US, you can start to consider self-employment. You will be expected to have proof that you can support yourself fully outside that investment, however.
Finally, does the visa requirement put you at a disadvantage? Absolutely.
You can expect to pay between US $10K and $20K, if you move alone without significant furniture, in direct moving costs; unless you want to foot that entirely alone you are asking a non-trivial investment from the company. Hardly extortionate, of course, and no more than a recruitment agency might get paid, but still more than a local.
You are also asking them to foot what probably amounts to the same sort of figure in legal costs, paperwork costs, staff time dealing with paperwork, and other expenses in getting you the visa.
Finally, unless you can become a permanent resident you are asking them to face ongoing costs relating to visa renewal - at least, time for you to renew, and probably more legal and paperwork costs on top of that.
Oh, and you are likely to either start remotely, or start with several months more delay than local workers would; that never helps. (Plus another $10K or so to fly you over for an interview, if they want to do that.)
All that covers just the hard practical side, though, and you have to remember that some employers will assume that, for example, a foreign worker is going to go home eventually (and forget that locals will change jobs), so you will face some potential additional biases on that front.
Don't be discouraged, though: you absolutely can do it, and it can be awesome. (You might also consider New York, and the rest of the east coast, since there is a lot more finance employment over there - and the thing that most helps is having skills that locals don't.)