You should retake General Physics 1 this summer and learn the material. I would ignore the Calc1 poor grade since you did better in Calc2. Or does Calc 3 terrify you ? It is really different and 2x harder than Calc 2 which is 2x harder than Calc 1.
You are basically on a 5 year plan for engineering. So 4 more years … I don’t even think summers would get you out in 4 or 4.5 years, too many courses with prerequisites. If you try to “catch up”, your odds get very low.
Mechanical is an odd and difficult choice for someone who did not do well in Physics 1 or Calc 1 (2 is OK, but should have been better and yes you need derivatives).
Physics 2 is electromagnetism … which might be easier, for you, and let you head down an EE path.
ChemE … well, why no chemistry ?
And you need to actually somehow convince the department, that is maybe limited enrollment, that you deserve a shot at taking engineering classes. Personally, I probably would not take you in preference over anyone with better physics or calc grades or who had taken more of the freshman engineering program and done well.
Next year, take Physics2, Chemistry, programming, intro to engineering, computer aided design and manufacturing, and start on the sophomore curriculum.
The flow charts are on line, so you can work through it yourself. If you do, and then go talk to the department with a plan on how to attack the first few years, maybe they will let you in, even provisionally. That would get you into a few intro to engineering classes so you can see what is involved.Then if you have good grades next year, you can start on say the semester 3 and 4 curriculum.
Getting buy in from your school’s department is going to be necessary to get approval anyway, so take advantage of their advice as well.
Engineering has its advantages which are often touted, but it is a difficult major which is equivalent to 5 years of most majors. So, without good prep and good results freshman year, you need 5 years … and there are easier paths.
I would also seriously consider what you are interested in, your main goals in life whether financial security, independence, whatever, and pick a major that suits you.