I'm working hard to make extra money to go visit her and eventually want to stay there. I don't want to be a burden to anyone and am obviously able to work.
The problem is that it's not that simple. You can't just move to the UK because you want to and because you 'can' work. You need to get a visa first.
You also can't just come to live with your partner - you would need to get married If you were able to qualify for a fiance or spousal visa, you would either need to marry within 6 months (fiance visa) or already be married before you applied (spousal visa).
Your visa options would be:
Tier 2 Sponsored Work Visa: (
https://www.gov.uk/tier-2-general/overview)
In order for a UK company to sponsor you for a visa to work for them, they must show that either:
a) The job is listed on the
Tier 2 Skills Shortage list, at the appropriate salary
or
b) That they have advertised the job for a minimum length of time across the UK and all other 26 EU countries (that's 500 million people) and could not find a single suitable applicant before they can hire you.
With unemployment still fairly high and so many people in the EU, you're very unlikely to be able to get a sponsored work visa unless you have very specialised skills or you work in a shortage occupation.
Tier 4 Student visa: (
https://www.gov.uk/tier-4-general-visa/overview)
- you could come to the UK to study for another degree. However, this is a very expensive option... you would need about $30,000 available to you for the first year of tuition and living expenses in order to qualify for the visa
Fiance/Spousal visa: (
https://www.gov.uk/join-family-in-uk/overview)
- you would need to either be getting married (and be planning a UK wedding) for a fiance visa or already married for a spousal visa
- she would need to meet the income requirement. Child maintenance can be used towards Category C: Non-Employment Income, but it sounds like it won't be enough since she has other benefits and those benefits likely can't be counted towards the £18,600
- Do you have any non-employment income in the US (rent from property you own, interest from stocks and shares etc.), or a 401K that could be used for the savings requirement?