A news conference called here to explain the mysterious hospitalization last week of Sen. Paula Hawkins (R-Fla.) raised almost as many questions as it answered today.

Dr. Blaine S. Nashold Jr., a neurosurgeon at Duke University Medical Center, said that Hawkins has been undergoing extensive tests here since last Thursday, when her office announced she had "gone on vacation," and that she may need major spinal surgery to correct "chronic" pain she suffers in her neck and lower back as result of an accident four years ago.

Nashold said he also is making "readjustments" in medications that Hawkins, 59, has been taking for high blood pressure and a long-term kidney disorder. It was the first hint that the senator suffered such ailments.

Hawkins, who is in a tough reelection fight, did not appear at the news conference, but issued a statement from her bedside that "I feel fine."

Surgery would keep Hawkins from her senatorial duties and from campaigning for about a month, Nashold said. But he said he will be unable to complete tests necessary to determine if the surgery is needed until the senator returns to the hospital from a highly charged political trip to Florida next week.

The explanation given for the secrecy around the senator's hospitalization was a desire to "protect her privacy."

"We weren't trying to hide anything. We weren't playing any games," said Thomas Kleppe, Hawkins' administrative assistant. "The lady was in pain."

Reporters in Florida began searching for Hawkins after she failed to appear for President Reagan's State of the Union address. First, they were told she had gone on vacation. Last Friday, spokesmen said she had been hospitalized for tests on her recurring back and neck pains, but refused to give details.

When one reporter, acting on a tip, telephoned last weekend to find if Hawkins was at Duke, a nurse said, "She's here, but under an assumed name."

The hunt spawned unfounded rumors that Hawkins' health problems would lead her to withdraw from her reelection race against Florida Gov. Bob Graham (D).

Hawkins' doctor, Nashold, said, "I don't think there was any mystery [in her hospitalization]. It was a straight referral from her doctors in Florida. They weren't making any progress."

Hawkins has undergone a cycle of medication, exercise, traction and pain since a room divider fell and hit her on the back of the neck while she was being interviewed at an Orlando television station four years ago. In 1960, after an auto accident, she had a disc fused in her neck.

In recent months, Hawkins reportedly has spent from 60 to 90 minutes a day in therapy. She has said she occasionally takes painkillers that make her feel like "you can't function fully."

Hawkins recently filed suit against WESH-TV in Orlando to recover medical costs, claiming among other things that her husband had lost her "consortium."

Nashold today refused to name the painkillers Hawkins has been taking. He described them as medications that "you can buy at any drugstore." The neurosurgeon described Hawkins as "in basically good health."

He said a decision on surgery will be made after she is given a myelogram, a spinal X-ray, when she returns from a Senate subcommittee hearing scheduled next Monday in Fort Lauderdale.

The subject of the hearing is a Florida pipeline that Hawkins has made a major issue in her reelection fight. Graham, who leads Hawkins in polls, today wished her a "speedy and full recovery."

In Florida, a news conference called by Rep. Connie Mack III (R-Fla.) was unusually well attended because of the rumors surrounding his possible entry into the Senate race if Hawkins was dropping out. There was much unhappiness among the Florida reporters when they found out the purpose was to unveil Mack's alternative to Gramm-Rudman-Hollings.

Some reporters accused Mack's staff of misleading them by refusing to say what the news conference was about. He replied that he would talk to his staff, and noted he had scheduled his news conference before Hawkins announced hers.