I only really know one Professor from last semester (I’m a second semester freshman now and applying to transfer in the fall) who’s going to write me a letter. But this Spring I’m taking classes that fit more with what I’m going to study, I know one of the Professors pretty well, and I have a month and a half until most application deadlines. Are they allowed to write a letter of Recommendation since I haven’t been in their class for a full semester?
Yes, of course they are! In fact, it’s better to have someone who can write a genuinely great “testimonial” for you, rather than a professor you’ve had for, say, two semesters but can only write the generic “Joe was a good student”-type recommendation.
Your professor will guide you by his (or her) response – i.e., he might express hesitancy if he doesn’t feel he can write credibly in your favor. Excepting that reaction, I agree with the advice above.
You most certainly can. I’m in a similar situation; second semester student asking for rec letters. I was relieved to find out that my professors were more than happy to write them! You should always let them know in advance. A month and a half is a good amount of time, I’d say.
Visit them during office hours and ask, I hope you’ll be pleasantly surprised like I was 
If you still have time you should try to go to office hours (even if you don’t help). That way you can talk to your professors more and it’ll make you seem more motivated. Also, someone told me if you still don’t know a professor that well them to bring them a resume with your goals and stuff that way they can write a more personal recommendation.
Thanks everyone for the advice. What actually happened was I talked with a Professor when asking him to sign my midterm report and he offered to write me a recommendation. So that was pretty sweet.