If you are going to make this work, you will need an incredible amount of family and friends support to be raising your child while you are in classes and on clinicals. Do not kid yourself that you can do this on your own - with a 10 month old, you cannot.
Paramedic school is not easy, and it shouldn't be - people's well-being and lives are in our hands. Ask yourself - if you or your son were in an accident, and needed life-saving care, do you want the medic who put the bare minimum in to pass, or do you want the medic who excelled? My guess is you want the medic who excelled. You have a number of issues to juggle - who is going to take care of your child while you are at work? Who will take care of your child while you are in class? Who will take care of your child while you are doing homework and studying? Who will take care of your child while you are on clinicals? How are you going to finance child care and medic school? All are tough questions.
Also, remember - you cannot come home from a clinical shift and expect to be able to properly care for your child for the next 12 hours, and then go back on shift. Clinicals are stressful learning times, and you will need to have some downtime to absorb what you are learning. You said "I wouldn't let someone else to raise my little boy." The reality is, someone else will have to be involved a great deal in raising your little boy, so you will have the time to devote to classes and studies.
Hard work could make this a reality, but there are going to be sacrifices. Maybe you can do your medic classes over an extended term - take 1 or 2 years more than a regular program, so you can fit in raising your son and working. Maybe you can consider delaying school until your boy is a little older and you can find quality care for him while you are in classes.
I'm not saying "no, it can't be done." I am saying "please look at all the options, and all the obstacles, before you jump in." You want to be the best medic you can be, not a bare minimum medic, so you have to make sure you have solved the obstacles before you start.
I'm not sure what you meant by "kiss my dream of a career goodbye." I don't know your age, but I suspect you are under 30 (correct me if I am wrong). Relax on the not having a career thing. For some reason, we all think we need to be established in a career by the time we are 24, and have the house, the picket fence, and the car by then. The reality is that the average person changes careers 3 or more times over a lifetime, and many return to school later in their careers to change careers. If it doesn't happen this year, it doesn't mean it can't happen at all.
Take a deep breath, and review all your options. Good to see you are asking for advice! You can take what people say, or leave it - remember, advice is what you pay for it... but at least it gives you more things to think about, and a more educated way to make a decision.
Wish you the best!