I guessed it was an HP because they are notorious for this, mine included !!!
first, speedfan wont work on many HPs because they dont put sensors in them for fan speed. Doesnt exist.
second, yes, the beeping is the motherboard warning you that the fan is malfunctioning and you are going to have over heating issues soon.
have you tried blowing out the vents ? it doesnt actually help much in these situations becuse the fan has already been damaged.
you can replace the fan assembly, replace the thermal past with better quality paste, and many other cooling techniques. check youtube for videos with tutorials.
i wont tell you what i did with mine, its much to risky, however, mine has lasted 2 years, since it started, for a total of 7 years, and no more warning signals.
bottom line, you have to have that fixed real soon. your cpu and video device are in jeopardy.