Lateral entry

Distance learning is not a good idea. You should take admission in a college through lateral entry and continue your higher education.

All private and government colleges take admission through LEET score, so you can try in all.

Yes, you can apply to IGNOU or SOL and complete your graduation through lateral entry. However, for lateral entry you might be required to provide proof for the reason of the GAP.

LEET is going to conducted by several universities and colleges separately to avail direct second year admissions. In general, their are requirements of Science with Mathematics at 10th standard and 60%(General) in Diploma/B.Sc.
As you are looking for different stream (not mentioned), Haryana LEET avails courses of several other streams like ceramic engineering, Food engineering, Bio. medical engineering, printing engineering etc.